The Collaborative International Dictionary of English v.0.48:

Smirk \Smirk\, v. i. [imp. & p. p. Smirked; p. pr. & vb. n.
   Smirking.] [OE. smirken, ASS. smercian, smearcian; cf. MHG.
   smieren, smielen, to smile. See Smile, v. i.]
   To smile in an affected or conceited manner; to smile with
   affected complaisance; to simper.
   [1913 Webster]