Waif
late Middle English: from an Anglo-Norman French variant of Old Northern French gaif, probably of Scandinavian origin. Early use was often in waif and stray, as a legal term denoting a piece of property found and, if unclaimed, falling to the lord of the manor.
wiktionary
The noun is derived from Late Middle English weif(“ownerless property subject to seizure and forfeiture; the right of such seizure and forfeiture; revenues obtained from such seizure and forfeiture”)[and other forms], [1] from Anglo-Norman waif, weif[and other forms] (compare Anglo-Latin waivum[and other forms], Medieval Latin waivium), possibly from Old French waif, a variant of gaif, gayf(“property that is lost and unclaimed; of property: lost and unclaimed”)(Norman)[and other forms], probably from a North Germanic source such as Old Norse veif(“flag; waving thing”), [2] from Proto-Germanic *waif-, from Proto-Indo-European *weyp-(“to oscillate, swing”).
The verb is derived from the noun. [3]
Possibly from Old Norse veif(“flag; waving thing”); [4] see further at etymology 1.
Origin unknown; possibly related to the following words: [5]
etymonline
waif (n.)
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.