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 *weip- "to turn, vacillate, tremble ecstatically" (see vibrate). 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.