Green’s Dictionary of Slang

1. unpleasant, dull, weak.

1953		W. Brown Run, Chico, Run (1959) 38: His partner wouldn’t be any droopy-looking blonde witch like his father had.
1992		G.P. Pelecanos Firing Offense 38: ‘I could have had that fifty-nine cent ice bucket over here months ago, but I thought I’d let his droopy ass stew about it for a while’.

2. depressed.

c.1943		‘Bill O. Lading’ You Chirped a Chinful!! n.p.: Droopy: Screwy.
1965		(con. 1930s) R. Wright Lawd Today 78: Well, ain’t that enough to be droopy about?
1996		J. Cameron It Was An Accident 244: The bird by me got droopy and went back to her Spumante.