Dictionary:

blear

  (blîr)

1. To blur or redden (the eyes).
2. To blur; dim.

Bleary.

[Middle English bleren.]

verb

To make dim or indistinct: becloud, bedim, befog, blur, cloud, dim, dull, eclipse, fog, gloom, mist, obfuscate, obscure, overcast, overshadow, shadow. See clear/unclear.

adjective

Not clearly perceived or perceptible: bleary, cloudy, dim, faint, foggy, fuzzy, hazy, indefinite, indistinct, misty, obscure, shadowy, unclear, undistinct, vague. See clear/unclear.

The verb has one meaning:

Meaning #1: make dim or indistinct
  Synonym: blur

The adjective blear has one meaning:

Meaning #1: tired to the point of exhaustion
  Synonyms: bleary, bleary-eyed, blear-eyed