Dim or blurred, especially of eyesight or vision; tired and unfocused, as from lack of sleep or illness.
Possibly from Middle English blere or blere-eyed (blear-eyed), related to Old English blēr (eyes running or watering). The word has been in English since at least the 14th century in forms like 'blear-eyed.'
Shakespeare used 'blear-eyed' to describe people, and the word is still perfect for that specific feeling when you wake up too early or have been crying—that unfocused, watery-eyed, can't-quite-see-straight sensation.
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