"over the side of a ship," late Old English, from the phrase ofor bord, from over + bord "side of a ship" (see board (n.2)). To throw (something) overboard in the figurative sense of "cast aside, discard, reject" is from 1640s. Figurative sense of "excessively, beyond one's means" (especially in phrase go overboard) is attested by 1931 in Damon Runyon.
he went overboard to please his in-laws
they dropped their garbage overboard
overawe
overbear
overbearing
overbite
overblown
overboard
overbook
overburden
overcast
overcautious
overcharge