1560s, "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 "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 for "something easy" is American English, c.1928.
To chat amiably and casually; chew the fat: making transatlantic calls just to shoot the breeze/ enjoying ourselves and shooting the breeze/ sit down on a bench and shoot the fat (1941+)