measure (v.)
c.1300, "to deal out by measure," from Old French mesurer "measure; moderate, curb" (12c.), from Late Latin mensurare "to measure," from Latin mensura "a measuring, a measurement; thing to measure by," from mensus, past participle of metiri "to measure," from PIE *me- (2) "to measure" (see meter (n.2)).

Replaced Old English cognate mæð "measure." Meaning "to ascertain spatial dimensions of" is mid-14c. To measure up "have the necessary abilities" is 1910, American English. Related: Measured; measuring.
measure (n.)
c.1200, "moderation, temperance, abstemiousness;" c.1300, "instrument for measuring," from Old French mesure "limit, boundary; quantity, dimension; occasion, time" (12c.), from Latin mensura "measure" (see measure (v.)). Meaning "size or quantity as ascertained by measuring" is from early 14c. Meaning "action of measuring; standard measure of quantity; system of measuring; appointed or alloted amount of anything" is late 14c. Also from late 14c. are senses "proper proportion, balance." Sense of "that to which something is compared to determine its quantity" is from 1570s. Meaning "rhythmic pattern in music" is late 14c.; from mid-15c. in poetry, c.1500 in dance. Meaning "treatment 'meted out' to someone" is from 1590s; that of "plan or course of action intended to obtain some goal" is from 1690s; sense of "legislative enactment" is from 1759. Phrase for good measure (late 14c.) is literally "ample in quantity, in goods sold by measure."