The Collaborative International Dictionary of English v.0.48:

Unbalanced \Un*bal"anced\, a. [In senses 1 and 2, pref. un- not
   + balanced; in sense 3, 1st pref. un- + balance.]
   1. Not balanced; not in equipoise; having no counterpoise, or
      having insufficient counterpoise.
      [1913 Webster]

            Let Earth unbalanced from her orbit fly. --Pope.
      [1913 Webster]

   2. (Com.) Not adjusted; not settled; not brought to an
      equality of debt and credit; as, an unbalanced account;
      unbalanced books.
      [1913 Webster]

   3. Being, or being thrown, out of equilibrium; hence,
      disordered or deranged in sense; unsteady; unsound; as, an
      unbalanced mind. --Pope.
      [1913 Webster]

WordNet (r) 3.0 (2006):

unbalanced
    adj 1: being or thrown out of equilibrium [syn: unbalanced,
           imbalanced] [ant: balanced]
    2: affected with madness or insanity; "a man who had gone mad"
       [syn: brainsick, crazy, demented, disturbed, mad,
       sick, unbalanced, unhinged]
    3: debits and credits are not equal