1960s, probably an alteration of pussy (n.2). DAS suggests shortened from hypothetical pussy-wussy, reduplicated form of pussy (n.1).
1982, abbreviated from wussy.
Mike Damone: You are a wuss: part wimp, and part pussy ["Fast Times at Ridgemont High" script, 1982]
A weak person; pussycat, wimp: 6 Ways Not to be a Wuss/ ''Wussy'' was a particularly expressive word, the handy combination of wimp and pussy
[1960s+ Teenagers; perhaps a shortening of hypothetical pussy-wussy]