late 15c., "size of the body" (a sense now obsolete), from Old French corsage "bust, trunk, body" (12c.), from cors "body," from Latin corpus "body" (from PIE root *kwrep- "body, form, appearance").
The meaning "body of a woman's dress, bodice" is from 1818 in fashion plates translated from French; by 1843 in a clearly English context. Sense of "a bouquet worn on the bodice" is 1911, American English, apparently from French bouquet de corsage "bouquet of the bodice."