1960s, probably an alteration of pussy (n.2). DAS suggests shortened from hypothetical pussy-wussy, reduplicated form of pussy (n.1).
Entries linking to wussy
pussy n.2
slang for "female pudenda," by 1879, but probably older; perhaps from Old Norse puss "pocket, pouch" (compare Low German puse "vulva"), or perhaps instead from the cat word (see pussy (n.1)) on the notion of "soft, warm, furry thing;" compare French le chat, which also has a double meaning, feline and genital. Earlier uses are difficult to distinguish from pussy (n.1), e.g.:
The word pussie is now used of a woman [Philip Stubbes, "The Anatomie of Abuses," 1583]
And songs such as "Puss in a Corner" (1690, attributed to D'Urfey) clearly play on the double sense of the word for ribald effect. But the absence of pussy in Grose and other early slang works argues against the vaginal sense being generally known before late 19c., as does its frequent use as a term of endearment in mainstream literature, as in:
"What do you think, pussy?" said her father to Eva. [Harriet Beecher Stowe, "Uncle Tom's Cabin," 1852]
Pussy-whipped "hen-pecked" is attested by 1956 (Middle English had cunt-beaten "impotent," in reference to a man, mid-15c.).
pussy n.1
"cat," by 1690s, a diminutive of puss (n.1), also used of a rabbit (1715). As a term of endearment for a girl or woman, from 1580s (also used of effeminate men), and applied childishly to anything soft and furry. To play pussy was World War II RAF slang for "take advantage of cloud cover, jumping from cloud to cloud to shadow a potential victim or avoid recognition."
wuss n.
1982, abbreviated from wussy.
Mike Damone: "You are a wuss: part wimp, and part pussy"