Yours, Etc.: Origins and Uses of 8 Sign-Offs
c.1300, blere "watery, rheumy," perhaps related to blur. Cf. Middle High German blerre "having blurred vision."
"to dim (of vision); to have watery or rheumy eyes," early 14c., of uncertain origin, possibly from an Old English *blerian, from the same source as blear (adj.). Related: Bleared; blearing.