The Collaborative International Dictionary of English v.0.48:

Stuck-up \Stuck"-up`\, a.
   Self-important and supercilious, ?onceited; vain; arrogant.
   [Colloq.]
   [1913 Webster]

         The airs of small, stuck-up, men.        --A. K. H.
                                                  Boyd.
   [1913 Webster]

WordNet (r) 3.0 (2006):

stuck-up
    adj 1: (used colloquially) overly conceited or arrogant; "a
           snotty little scion of a degenerate family"-Laurent Le
           Sage; "they're snobs--stuck-up and uppity and
           persnickety" [syn: bigheaded, persnickety, snooty,
           snot-nosed, snotty, stuck-up, too big for one's
           breeches, uppish]