Old English weosule, wesle "weasel," from Proto-Germanic *wisulon (cf. Old Norse visla, Middle Dutch wesel, Dutch wezel, Old High German wisula, German Wiesel), probably related to Proto-Germanic *wisand- "bison" (see bison), with a base sense of "stinking animal," because both animals have a foul, musky smell (cf. Latin vissio "stench"). A John Wesilheued ("John Weaselhead") turns up on the Lincolnshire Assize Rolls for 1384, but the name seems not to have endured, for some reason.
"to deprive (a word or phrase) of its meaning," 1900, from weasel (n.); so used because the weasel sucks out the contents of eggs, leaving the shell intact; the sense of "extricate oneself (from a difficult place) like a weasel" is first recorded 1925; that of "to evade and equivocate" is from 1956.