The Collaborative International Dictionary of English v.0.48:

Unweeting \Un*weet"ing\, a. [See Un- not, and Weet, Wit.]
   Unwitting. [Obs.] --Chaucer. Spenser.
   [1913 Webster] -- Un*weet"ing*ly, adv. [Obs.] --Milton.
   [1913 Webster]