"From Middle English mete, from Old English mete (“food”), from Proto-West Germanic *mati, from Proto-Germanic *matiz (“food”), from Proto-Indo-European *meh₂d- (“to drip, ooze; grease, fat”). Cognate with West Frisian mete, Old Saxon meti, Old High German maz (“food”), Icelandic matur, Swedish mat, Danish mad, Gothic 𐌼𐌰𐍄𐍃 (mats).

A -ja- derivation from the same base is found in Middle Dutch and Middle Low German met (“lean pork”), from which Dutch met (“minced pork”) and German Mett (“minced meat”) derive, respectively. Compare also Old Irish mess (“animal feed”) and Welsh mes (“acorns”), English mast (“fodder for swine and other animals”), which are probably from the same root."

From Wiktionary.