"four-wheeled vehicle to carry heavy loads," late 15c., from Middle Dutch wagen, waghen, from Proto-Germanic *wagna- (source also of Old English wægn, Modern English wain, Old Saxon and Old High German wagan, Old Norse vagn, Old Frisian wein, German Wagen), from PIE *wogh-no-, suffixed form of root *wegh- "to go, move, transport in a vehicle" (source also of Latin vehiculum). It is thus related to way.

In Dutch and German, it is the general word for "a wheel vehicle;" its use in English is a result of contact through Flemish immigration, Dutch trade, or the Continental wars. It has largely displaced the native cognate, wain. Spelling preference varied randomly between -g- and -gg- from mid-18c., until American English settled on the etymological wagon, while waggon remained common in Great Britain. Wagon-train is attested from 1810. Phrase on the wagon "abstaining from alcohol" is attested by 1904, originally on the water cart.

c. 1500, kind of small bird that has its tail in continuous motion (late 12c. as a surname), earlier wagstart (mid-15c.), from wag (v.) + tail (n.). From 18c. as "a harlot," but this sense seems to be implied much earlier:

If therefore thou make not thy mistress a goldfinch, thou mayst chance to find her a wagtaile. [Lyly, "Midas," 1592]

late 14c., "unclaimed property, flotsam, stray animal," from Anglo-French waif (13c., Old French guaif) "ownerless property, something lost;" as an adjective, "not claimed, outcast, abandoned," probably from a Scandinavian source akin to Old Norse veif "waving thing, flag," from Proto-Germanic *waif-, from PIE root *weip- "to turn, vacillate, tremble ecstatically." Compare Medieval Latin waivium "thing thrown away by a thief in flight." A Scottish/northern English parallel form was wavenger (late 15c.).

Meaning "person (especially a child) without home or friends" first attested 1784, from legal phrase waif and stray (1620s), from the adjective in the sense "lost, strayed, homeless." Neglected children being uncommonly thin, the word tended toward this sense. Connotations of "fashionable, small, slender woman" began 1991 with application to childishly slim supermodels such as Kate Moss.