The Collaborative International Dictionary of English v.0.48:

bleary-eyed \bleary-eyed\ adj.
   having eyes sore or unfocused, due to weariness or excessive
   drinking; same as blear-eyed[1].

   Syn: blear, bleary.
        [WordNet 1.5]

   2. same as teary. [R.]
      [PJC]

WordNet (r) 3.0 (2006):

bleary-eyed
    adj 1: tired to the point of exhaustion [syn: bleary, blear,
           bleary-eyed, blear-eyed]