waste (v.) Look up waste at Dictionary.com
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, waste" (see vain). 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.) Look up waste at Dictionary.com
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 "waste" (see waste (v.)).

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.) Look up waste at Dictionary.com
c.1300, of land, "desolate, uncultivated," from Anglo-French and Old North French waste (Old French gaste), from Latin vastus (see waste (v.)). From c.1400 as "superfluous, excess;" 1670s as "unfit for use." Waste-paper attested from 1580s.