The noun is borrowed from Scots caddie (“military cadet; young man; ragamuffin; person engaged to run errands; person hired to assist a golfer”), from French cadet (“army cadet; younger sibling”), from capdet (“captain; chief”) (Gascony, archaic), from Late Latin capitettum, from Latin caput (“head”), ultimately from Proto-Indo-European *kap- (“head”). Doublet of cadel, cadet, capital, capitellum, and caudillo.
The verb is derived from the noun.