1860, "to remain clinging," 1860, especially "cling fondly to" (1871); see hang (v.) + on (adv.). As a command to be patient, wait a minute, from 1936, originally in telephone conversations.
Please hang on while I get your folder
hand-written
handy
handyman
hang
hang in
hang on
hang out
hang up
hangar
hang-dog
hanged