"foresail of a ship," 1660s, gibb, of uncertain origin, perhaps related to gibbet, from notion of a sail "hanging" from a masthead [Barnhart, OED]. Or perhaps from jib (v.) "shift a sail or boom" (1690s), from Dutch gijben, apparently related to gijk "boom or spar of a sailing ship." Said to indicate a ship's character to an observant sailor as a strange vessel approaches at sea; also nautical slang for "face," hence cut of (one's) jib "personal appearance" (1821).
One's general appearance or personality, as in I don't like the cut of Ben's jib. In the 17th century the shape of the jib sail often identified a vessel's nationality, and hence whether it was hostile or friendly. The term was being used figuratively by the early 1800s, often to express like or dislike for someone.