1920 (but not attested again until 1960), perhaps a clipped form of whimper (cf whimp, 1540s), perhaps influenced by J. Wellington Wimpy, comparatively unaggressive character in "Popeye" comics.
wimp (v.)
1986, with out (adv.), from wimp (n.). Related: Wimped; wimping.
willy-nilly
Wilsonian
wilt
wily
Wimbledon
wimp
wimple
wimpy
win
wince
winch