The story
“Cute” is short for “acute,” meaning sharp-witted, and “button” has meant something small and sweet since the late 1600s, as in a 1696 line about “such a little Button of a World.” The older “bright as a button” was around by the late 1700s. “Cute as a button” turns up in a 1913 New Mexico newspaper, praising a boy playing Little Lord Fauntleroy.