The original long vowel (preserved in breathe) has become short. Meaning "ability to breathe," hence "life" is from c. 1300. Meaning "a single act of breathing" is from late 15c.; sense of "the duration of a breath, a moment, a short time" is from early 13c. Meaning "a breeze, a movement of free air" is from late 14c.
"to draw air into and expel it from the lungs; to inhale and exhale (a scent, etc.)," c. 1200, not in Old English, but it retains the original Old English vowel of its source word, breath. To breathe (one's) last "die" is from 1590s. To breathe down the back of (someone's) neck "be close behind" is by 1946. Related: Breathed; breathing.