1560s, "moderate north or northeast wind," from Old Spanish briza "cold northeast wind;" in West Indies and Spanish Main, the sense shifting to "northeast trade wind," then "brisk, fresh wind from the sea." English sense of "gentle or light wind" is from 1620s. An alternative possibility is that the English word is from East Frisian brisen "to blow fresh and strong." The slang sense of "something easy" is American English, c. 1928.
1680s, "blow gently," from breeze (n.). Meaning "move briskly" is from 1904. Related: Breezed; breezing.