The Collaborative International Dictionary of English v.0.48:

Flimsy \Flim"sy\, a. [Compar. Flimsier; superl. Flimsiest.]
   [Cf. W. llymsi naked, bare, empty, sluggish, spiritless. Cf.
   Limsy.]
   Weak; feeble; limp; slight; vain; without strength or
   solidity; of loose and unsubstantial structure; without
   reason or plausibility; as, a flimsy argument, excuse,
   objection.
   [1913 Webster]

         Proud of a vast extent of flimsy lines.  --Pope.
   [1913 Webster]

         All the flimsy furniture of a country miss's brain.
                                                  --Sheridan.

   Syn: Weak; feeble; superficial; shallow; vain.
        [1913 Webster]