c. 1300, from Old Norse veikr "weak," cognate with Old English wac "weak, pliant, soft," from Proto-Germanic *waika- "yield" (source also of Old Saxon wek, Swedish vek, Middle Dutch weec, Dutch week "weak, soft, tender," Old High German weih "yielding, soft," German weich "soft"), from PIE root *weik- (2) "to bend, to wind."
Sense of "lacking authority" is first recorded early 15c.; that of "lacking moral strength" late 14c. In grammar, denoting a verb inflected by regular syllabic addition rather than by change of the radical vowel, from 1833. Related: Weakly. Weak-kneed "wanting in resolve" is by 1856; older in a literal sense.