"to allot," Old English metan (West Saxon mæton), "to measure, ascertain the dimension or quantity of; measure out; compare; estimate the greatness of value of" (class V strong verb; past tense mæt, past participle meten), from Proto-Germanic *metana "to measure" (source also of Old Saxon metan, Old Frisian, Old Norse meta, Dutch meten, Old High German mezzan, German messen, Gothic mitan "to measure"), from PIE root *med- "take appropriate measures." Meaning "distribute or apportion by measure" is from c. 1300 and is the surviving sense, used now exclusively with out. Related: Meted; meting.
by c. 1400, "a goal" (a sense now obsolete); late 15c. (Caxton) "a boundary, limit, boundary mark," from Old French mete "limit, bounds, frontier" and directly from Latin mēta "goal, boundary, post, pillar," which is of uncertain origin. Surviving only in plural, in the phrase metes and bounds (Anglo-Latin metis et bundis, early 14c.)