The Collaborative International Dictionary of English v.0.48:

Twiggy \Twig"gy\, a.
   Of or pertaining to a twig or twigs; like a twig or twigs;
   full of twigs; abounding with shoots. " Twiggy trees."
   --Evelyn.
   [1913 Webster]

WordNet (r) 3.0 (2006):

twiggy
    adj 1: thin as a twig [syn: twiggy, twiglike]