Waste
Middle English: from Old Northern French wast(e ) (noun), waster (verb), based on Latin vastus ‘unoccupied, uncultivated’.
wiktionary
From Middle English waste(“a waste”, noun), from Anglo-Norman, Old Northern French wast, waste(“a waste”), from Frankish *wōstī(“a waste”), from Proto-Indo-European *h₁weh₂-(“empty, wasted”).
From Middle English waste(“waste”, adjective), from Anglo-Norman, Old Northern French wast(“waste”), from Frankish *wōstī(“waste, empty”), from Proto-Indo-European *wāsto-(“empty, wasted”). Cognate with Old High German wuosti, wuasti(“waste, empty”), Old Saxon wōsti(“desolate”), Old English wēste(“waste, barren, desolate, empty”).
From Middle English wasten(“to waste, lay waste”), from Anglo-Norman, Old Northern French waster(“to waste, devastate”) (compare also the variant gaster and French gâter from a related Old French word); the Anglo-Norman form waster was either from Frankish *wōstijan(“to waste”), from Proto-Indo-European *wāsto-(“empty, wasted”), or alternatively from Latin vastāre, present active infinitive of vastō and influenced by the Frankish; the English word was assisted by similarity to native Middle English westen("to waste"; > English weest). Cognate with Old High German wuostan, wuastan, wuostjan(“to waste”) (Modern German wüsten), Old English wēstan(“to lay waste, ravage”).
etymonline
waste (v.)
c. 1200, "devastate, ravage, ruin," from Anglo-French and Old North French waster "to waste, squander, spoil, ruin" (Old French gaster; Modern French gâter), altered (by influence of Frankish *wostjan) from Latin vastare "lay waste," from vastus "empty, desolate," from PIE *wasto-, extended suffixed form of root *eue- "to leave, abandon, give out." Related: wasted; wasting.
The Germanic word also existed in Old English as westan "to lay waste, ravage." Spanish gastar, Italian guastare also are from Germanic. Meaning "to lose strength or health; pine; weaken" is attested from c. 1300; the sense of "squander, spend or consume uselessly" is first recorded mid-14c.; meaning "to kill" is from 1964. Waste not, want not attested from 1778.
waste (n.)
c. 1200, "desolate regions," from Anglo-French and Old North French wast "waste, damage, destruction; wasteland, moor" (Old French gast), from Latin vastum, neuter of vastus "empty, desolate," from PIE *wasto-, extended suffixed form of root *eue- "to leave, abandon, give out."
Replaced or merged with Old English westen, woesten "a desert, wilderness," from the Latin word. Meanings "consumption, depletion," also "useless expenditure" are from c. 1300; sense of "refuse matter" is attested from c. 1400. Waste basket first recorded 1850.
waste (adj.)
c. 1300, of land, "desolate, uncultivated," from Anglo-French and Old North French waste (Old French gaste), from Latin vastus "empty, desolate," from PIE *wasto-, extended suffixed form of root *eue- "to leave, abandon, give out." From c. 1400 as "superfluous, excess;" 1670s as "unfit for use." Waste-paper attested from 1580s.
