Vat

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Middle English: southern and western dialect variant of obsolete fat ‘container’, of Germanic origin; related to Dutch vat and German Fass .

wiktionary

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From Middle English vat, a dialectal variant of fat(“vat, vessel, cask”), from Old English fæt(“vat, vessel”), from Proto-Germanic *fatą(“vessel”), from Proto-Indo-European *pod-(“vessel”). Cognate with Scots fat, vat, vautt(“vat, cask, tub”), West Frisian fet, Dutch vat(“barrel, cask, vessel, vat”), German Fass(“barrel, keg, drum, cask, vat”), Danish fad(“saucer, dish”), Swedish fat(“dish, barrel, cask, vat”), Icelandic fat(“dish, saucer”). See fat.

etymonline

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vat (n.)

c. 1200, large tub or cistern, "especially one for holding liquors in an immature state" [Century Dictionary], southern variant (see V) of Old English fæt "container, vat," from Proto-Germanic *fatan (source also of Old Saxon, Old Norse fat, Old Frisian fet, Middle Dutch, Dutch vat, Old High German faz, German faß), from PIE root *ped- (2) "container" (source also of Lithuanian puodas "pot").