Online Etymology Dictionary

fill (v.): Old English fyllan "to fill, make full, fill up, replenish, satisfy; complete, fulfill," from Proto-Germanic *fulljan "to fill" (source also of Old Saxon fulljan, Old Norse fylla, Old Frisian fella, Dutch vullen, German füllen, Gothic fulljan "to fill, make full"), a derivative of adjective *fullaz "full" (see full (adj.)). Related: Filled.

To fill the bill (1882) originally was U.S. theatrical slang, in reference to a star of such magnitude his or her name would be the only one on a show's poster. To fill out "write in required matter" is recorded from 1880.
fill (n.): mid-13c., fille, "a full supply," from Old English fyllu "fullness, 'fill,' feast, satiety," from Proto-Germanic *full-ino- "fullness" (source also of Old High German fulli, German Fülle, Old Norse fyllr), noun of state from *fullaz "full" (see full (adj.)). Meaning "extra material in music" is from 1934.
fill-in (n.): "substitute," 1918 (as an adjective, 1916), from verbal phrase; see fill (v.), in (adv.). Earlier as a noun was fill-up (1811).
filler (n.): late 15c., "one who fills," agent noun from fill (v.). Meaning "something used to fill" is from 1590s. Specifically of food products by 1901.
fillet (n.): early 14c., "little headband," from Old French filet "thread, filament; strip, ligament" (12c.), diminutive of fil "thread" (see file (v.1)). Sense of "cut of meat or fish" is from late 14c., apparently so called because it was prepared by being tied up with a string.
fillet (v.): c. 1600, "to bind with a narrow band," from fillet (n.). Meaning "to cut in fillets" is from 1846. Related: Filleted; filleting.
filling (n.): c. 1400, "that which fills or fills up," verbal noun from fill (v.). Dentistry sense is from 1848. Filling station attested by 1915.
filling (adj.): "calculated to fill or satisfy," 1620s, present-participle adjective from fill (v.).
fillip (v.): mid-15c., philippen "to flip something with the fingers, snap the fingers," possibly of imitative origin. As a noun, from 1520s, fyllippe.
filly (n.): c. 1400, filli, fyly, "a young mare, female colt or foal," possibly from Old Norse fylja, fem. of foli "foal" (see foal (n.)). Slang sense of "lively young girl" is from 1610s.
film (n.): Old English filmen "membrane, thin skin, foreskin," from West Germanic *filminjan (source also of Old Frisian filmene "skin," Old English fell "hide"), extended from Proto-Germanic *fello(m) "animal hide," from PIE *pel- (4) "skin, hide" (source also of Greek pella, Latin pellis "skin").

Sense of "a thin coat of something" is 1570s, extended by 1845 to the coating of chemical gel on photographic plates. By 1895 this also meant the coating plus the paper or celluloid. Hence "a motion picture" (1905); sense of "film-making as a craft or art" is from 1920.
film (v.): c. 1600, "to cover with a film or thin skin," from film (v.). Intransitive sense is from 1844. Meaning "to make a movie of" is from 1899. Related: Filmed; filming.
film noir (n.): 1958, from French, literally "black film," from noir (12c.), from Latin niger (see Negro).
film-maker (n.): also filmmaker, 1859 as a solution used in developing photographs, later "a producer of film for cameras" (by 1889), from film (n.) + maker. As "producer of a cinematographic work, movie-maker," from 1905.
film-strip (n.): also filmstrip, 1930, from film (n.) + strip (n.).
filmography (n.): 1962, from film (n.) + ending from bibliography, etc.
filmy (adj.): c. 1600, "composed of thin membranes," from film (n.) + -y (2). Related: Filminess.
filter (n.): early 15c., "piece of felt through which liquid is strained," from Old French feutre "felt, felt hat, carpet" (Modern French filtre) and directly from Medieval Latin filtrum "felt" (used to strain impurities from liquid), from West Germanic *filtiz (see felt (n.)). Figurative use from c. 1600. As a pad of absorbent material attached to a cigarette, from 1908.
filter (v.): 1570s (transitive), from French filtrer or from Medieval Latin filtrare, from filtrum "felt" (see filter (n.)). The figurative sense is from 1830. Intransitive use from 1798. Related: Filtered; filtering.
filth (n.): Old English fylð "uncleanness, impurity, foulness," from Proto-Germanic *fulitho (source also of Old Saxon fulitha "foulness, filth," Dutch vuilte, Old High German fulida), noun derivative of *fulo- "foul" (see foul (adj.)). A classic case of i-mutation.
filthy (adj.): late 12c., fulthe, "corrupt, sinful," from filth + -y (2). Meaning "physically unclean, dirty, noisome" is from late 14c. Meaning "morally dirty, obscene" is from 1530s.
In early use often hardly more emphatic than the mod. dirty; it is now a violent expression of disgust, seldom employed in polite colloquial speech. [OED]
Related: Filthily; filthiness.
filtrate (v.): 1610s, probably a back-formation from filtration or else from Medieval Latin filtratus. Related: Filtrated; filtrating. As a noun, "liquid which has passed through a filter," from 1846.
filtration (n.): "act or process of filtering," c. 1600, perhaps from French filtration (1570s), noun of action from filter "to filter" (see filter (v.)).
fimbria (n.): "a fringing filament," from Late Latin fimbria (sing.), from Latin fimbriae (pl.), "fringe, border, threads." Related: Fimbriated (late 15c.); fimbrial.
fin (n.): Old English finn "fin," from Proto-Germanic *finno (source also of Middle Low German vinne, Dutch vin), perhaps from Latin pinna "feather, wing" (see pin (n.)); or, less likely, from Latin spina "thorn, spine" (see spine).

U.S. underworld slang sense of "$5 bill" is 1925, from Yiddish finif "five," from German fünf (see five) and thus unrelated. The same word had been used in England in 1868 to mean "five pound note" (earlier finnip, 1839).
fin de siecle (adj.): 1890, from French fin de siècle "end of century," phrase used as an adjective. At the time it meant "modern;" now it means "from the 1890s." "App. first in title of a comedy, Paris fin de siècle, produced at the Gymnase, Feb. 1890" [Weekley]. French siècle "century, age" is from Latin saeculum (see secular).
finagle (v.): "get dishonestly or deviously," 1926, American English, possibly a variant of English dialectal fainaigue "to cheat or renege" (at cards), which is of unknown origin. Liberman says finagle is from figgle, phonetic variant of fiddle "fidget about," frequentative of fig. Related: Finagled; finagling.
final (adj.): early 14c., from Old French final "final, last," and directly from Late Latin finalis "of or pertaining to an end, concluding, final," from finis "end" (see finish (v.)). As a noun, late 14c., "that which comes last;" meaning "final contest" in a sporting sense is from 1880. As a shortening of final examination, from 1880.
final solution (n.): 1947, translation of German Endlösung, name given to Nazi Jewish policy from 1941.
finale (n.): 1783, a musical term, from noun use of Italian finale "final," from Latin finalis "of or pertaining to an end" (see final). From 1724 as an Italian word in English. Figurative use by 1810.
finalise (v.): chiefly British English spelling of finalize. For suffix, see -ize. Related: Finalised; finalising.
finalist (n.): "competitor remaining after eliminations," 1896, from final + -ist. Earlier "one who believes the end has been reached" (1883).
finality (n.): 1540s, "a goal, a guiding object," from Middle French finalité, from Late Latin finalitatem (nominative finalitas) "state of being final," from Latin finalis "last, of or pertaining to an end" (see final). From 1833 as "quality or state of being final."
finalize (v.): 1850, from final + -ize. Related: Finalized; finalizing.
finally (adv.): late 14c., fynaly "at the end;" c. 1400, "completely, beyond recovery;" from final + -ly (2).
finals (n.): short for final exams, by 1890; see final (adj.).
finance (n.): c. 1400, "an end, settlement, retribution," from Old French finance "end, ending; pardon, remission; payment, expense; settlement of a debt" (13c.), noun of action from finer "to end, settle a dispute or debt," from fin (see fine (n.)). Compare Medieval Latin finis "a payment in settlement, fine or tax."

The notion is of "ending" (by satisfying) something that is due (compare Greek telos "end;" plural tele "services due, dues exacted by the state, financial means"). The French senses gradually were brought into English: "ransom" (mid-15c.), "taxation" (late 15c.); the sense of "management of money, science of monetary business" first recorded in English 1770.
finance (v.): late 15c., "to ransom" (obsolete), from finance (n.). Sense of "to manage money" is recorded from 1827; that of "to furnish with money" is from 1866. Related: Financed; financing.
finances (n.): "pecuniary resources, funds in money," 1730, modeled on the French cognate, from plural of finance (n.).
financial (adj.): 1769, from finance (n.) + -ial. Related: Financially.
financier (n.): 1610s, "one concerned with finances" (especially public), from French financier (16c.), from finance (see finance (n.)). Sense of "capitalist, one skilled in financial operations" is first recorded 1867.
finch (n.): common European bird, Old English finc "finch," from Proto-Germanic *finkiz "finch" (source also of Middle Low German and Middle Dutch vinke, Dutch vink, Old High German finco, German Fink), perhaps imitative of the bird's note (compare Breton pint "chaffinch," Russian penka "wren").
find (v.): Old English findan "come upon, meet with; discover; obtain by search or study" (class III strong verb; past tense fand, past participle funden), from Proto-Germanic *finthan "to come upon, discover" (source also of Old Saxon findan, Old Frisian finda, Old Norse finna, Middle Dutch vinden, Old High German findan, German finden, Gothic finþan), originally "to come upon."

The Germanic word is from PIE root *pent- "to tread, go" (source also of Old High German fendeo "pedestrian;" Sanskrit panthah "path, way;" Avestan panta "way;" Greek pontos "open sea," patein "to tread, walk;" Latin pons (genitive pontis) "bridge;" Old Church Slavonic poti "path," peta "heel;" Russian put' "path, way").

Germanic *-th- in English tends to become -d- after -n-. The change in the Germanic initial consonant is from Grimm's Law. To find out "to discover by scrutiny" is from 1550s (Middle English had a verb, outfinden, c. 1300).
find (n.): "person or thing discovered, discovery of something valuable," 1825, from find (v.).
finder (n.): c. 1300, agent noun from find (v.).
finding (n.): c. 1300, "act of discovering" (by chance or after searching; also an instance of this); verbal noun from find (v.). From c. 1400 as "what the mind discovers; knowledge attained by human effort" (as distinct from revelation or authority). Late 14c. as "act of sustaining, supporting, or providing the necessities of life; that which is provided by way of sustenance and support." Legal sense "proceedings leading to a verdict in an inquisition, etc.," is from mid-15c. Old English finding meant "invention." Related: Findings.
fine (adj.): mid-13c., "unblemished, refined, pure, free of impurities," also "of high quality, choice," from Old French fin "perfected, of highest quality" (12c.), a back-formation from finire or else from Latin finis "that which divides, a boundary, limit, border, end" (see finish (v.)); hence "acme, peak, height," as in finis boni "the highest good." The English word is from c. 1300 as "rich, valuable, costly;" also in a moral sense "true, genuine; faithful, constant." From late 14c. as "expertly fashioned, well or skillfully made," also, of cloth, "delicately wrought." Of weapons or edges, "sharp" from c. 1400. In reference to quality of gold and silver, late 15c.

In French, the main meaning remains "delicate, intricately skillful;" in English since c. 1300 fine has been also a general broad expression of admiration or approval, the equivalent of French beau (as in fine arts, 1767, translating French beaux-arts). Related: Finer; finest. Fine print is from 1861 as "type small and close-set;" by 1934 in the extended sense "qualifications and limitations of a deal."
fine (n.): c. 1200, "termination, end; end of life," from Old French fin "end, limit, boundary; death; fee, payment, finance, money" (10c.), from Latin finis "end" (see finish (v.)), in Medieval Latin also "payment in settlement, fine or tax."

Modern meaning "exaction of money payment for an offense or dereliction" is via sense of "sum of money paid for exemption from punishment or to compensate for injury" (mid-14c., from the same sense in Anglo-French, late 13c.) and from phrases such as to make fine "make one's peace, settle a matter" (c. 1300). Meaning "sum of money imposed as penalty for some offense" is first recorded 1520s.
fine (v.): late 13c., "pay as a ransom or penalty," from fine (n.). Inverted meaning "to punish by pecuniary penalty" is from 1550s. Related: Fined; fining.
fine-toothed (adj.): c. 1600, "epicurean, having delicate tastes," from fine (adj.) + toothed "having teeth" (of a certain kind); see tooth (n.). By 1703 as "having fine teeth" (of a saw, file, comb, etc.); fine-tooth in this sense attested from 1804.