When “better half” appeared in the mid-16th century, it meant “the larger portion of something” or “more than half,” according to the Oxford English Dictionary. The usual sense now, which the OED defines as “a person’s husband, wife, or (in later use) partner,” appeared in the late 16th century. The first citation is from The Countesse of Pembrokes Arcadia, a pastoral romance by Sir Philip Sidney, published posthumously in 1590, four years after the author’s death: “My deare, my better halfe (said hee) I finde I must now leaue thee” (the dying Argalus is speaking here to his wife Parthenia). We should add that in the spousal sense, “better half” is often used affectionately or in a semi-humorous way.

Source: Grammarphobia