The Collaborative International Dictionary of English v.0.48:

Dizzy \Diz"zy\ (d[i^]z"z[y^]), a. [Compar. Dizzier
   (d[i^]z"z[i^]*[~e]r); superl. Dizziest.] [OE. dusi, disi,
   desi, foolish, AS. dysig; akin to LG. d["u]sig dizzy, OD.
   deuzig, duyzig, OHG. tusig foolish, OFries. dusia to be
   dizzy; LG. dusel dizziness, duselig, dusselig, D. duizelig,
   dizzy, Dan. d["o]sig drowsy, slepy, d["o]se to make dull,
   drowsy, d["o]s dullness, drowsiness, and to AS. dw[=ae]s
   foolish, G. thor fool. [root]71. Cf. Daze, Doze.]
   1. Having in the head a sensation of whirling, with a
      tendency to fall; vertiginous; giddy; hence, confused;
      indistinct.
      [1913 Webster]

            Alas! his brain was dizzy.            --Drayton.
      [1913 Webster]

   2. Causing, or tending to cause, giddiness or vertigo.
      [1913 Webster]

            To climb from the brink of Fleet Ditch by a dizzy
            ladder.                               --Macaulay.
      [1913 Webster]

   3. Without distinct thought; unreflecting; thoughtless;
      heedless. "The dizzy multitude." --Milton.
      [1913 Webster]