Old English bræð "odor, scent, stink, exhalation, vapor" (Old English word for "air exhaled from the lungs" was æðm), from Proto-Germanic *bræthaz "smell, exhalation" (source also of Old High German bradam, German Brodem "breath, steam"), perhaps from a PIE root *gwhre- "to breathe; smell."
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.
adjective suffix, "full of or characterized by," from Old English -ig, from Proto-Germanic *-iga- (source also of Dutch, Danish, German -ig, Gothic -egs), from PIE -(i)ko-, adjectival suffix, cognate with elements in Greek -ikos, Latin -icus (see -ic). Originally added to nouns in Old English; used from 13c. with verbs, and by 15c. even with other adjectives (for example crispy).
<a href="https://www.etymonline.com/word/breathy">Etymology of breathy by etymonline</a>
Harper, D. (n.d.). Etymology of breathy. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/breathy