abbreviation of ounce (n.1), 1540s, from Italian oz. (15c.), abbreviation of onza.
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ounce n.1
unit of weight, the twelfth part of a pound, early 14c., from Old French once, unce, a measure of weight or time (12c.), from Latin uncia "one-twelfth part" (of a pound, a foot, etc.), from Latin unus "one" (from PIE root *oi-no- "one, unique"). The Latin word had been adopted in Old English as ynce (see inch).
It was one-twelfth of a pound in the Troy system of weights, but one-sixteenth in avoirdupois. Abbreviation oz. is from older Italian onza. It was used loosely from late 14c. for "a small quantity." Also used in Middle English as a measure of time (7.5 seconds) and length (about 3 inches). In figurative expressions and proverbs, an ounce of X is compared or contrasted with a pound of Y from 1520s.