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late 14c., "act of plundering" (especially in war), from Old French pilage (14c.) "plunder," from pillier "to plunder, loot, ill-treat," possibly from Vulgar Latin *piliare "to plunder," probably from a figurative use of Latin pilare "to strip of hair," perhaps also meaning "to skin" (cf. figurative extension of verbs pluck, fleece), from pilus "a hair" (see pile (n.3)).
"plunder, despoil," 1590s, from pillage (n.). Related: Pillaged; pillaging. The earlier verb in English was simply pill (late Old English), which probably is from Latin pilare.
To eat voraciously or steal food: pillaged the office fridge when no one was looking