The Collaborative International Dictionary of English v.0.48:

Twill \Twill\ (tw[i^]l), v. t. [imp. & p. p. Twilled
   (tw[i^]l); p. pr. & vb. n. Twilling.] [Scotch tweel;
   probably from LG. twillen to make double, from twi- two; akin
   to AS. twi-, E. twi- in twilight. See Twice, and cf.
   Tweed, Tweel.]
   To weave, as cloth, so as to produce the appearance of
   diagonal lines or ribs on the surface.
   [1913 Webster]