1300-1400blear ‘to make (the eyes) unable to see clearly’(13-19 centuries)
Examples
EXAMPLES FROM OTHER DICTIONARIES
A messenger from the mill woke the bleary-eyed Thompson at 3:00 a.m.
EXAMPLES FROM THE CORPUS
Alexander wakes with a start, gives a visitor a perplexed, somewhat bleary stare, then melts blissfully back into slumber.
For most people breakfast is a time to renew contact with the world, often through bleary eyes at best.
I checked the clock, squinting through bleary eyes.
We pull on our coats with bleary yanks as the alcohol works its universal spell, and bump out the door.
unable to see very clearly, because you are tired or have been crying: Steve emerged from his room, unshaven and bleary-eyed.—blearily adverb—bleariness noun [uncountable]