late 14c., "unclaimed property, flotsam, stray animal," from Anglo-Norm. waif, gwaif (early 13c.) "ownerless property," 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). Cf. 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). 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, e.g. Kate Moss.