Green’s Dictionary of Slang

(orig. US) over-enthusiastic, very keen.

1927		H.C. Witwer Classics in Sl. 30: At this point, Ophelia, which it turned out really was overboard over Ham, gets cuckoo herself from listenin’ to him rave.
1941		Crisis Mar. 79: Americans have ‘gone overboard’ for the dances of our neighbor nations to the south.
1946		W.L. Gresham Nightmare Alley (1947) 229: The chump’s overboard.
1959		E. De Roo Young Wolves 49: ‘I don’t want to get all mixed up with you,’ he muttered. ‘You haven’t any choice. I’m overboard for you. You’re it. Everything I want.’.
1997		Smith & Standish Teaching Right and Wrong 25: Not that, in our society today, people have gone overboard for selfish hedonism and have jettisoned all the old morality.