1660s, "to cause to swell" (earlier, in reference to cured fish, "to cause to be soft," 1610s), from now obsolete bloat (adj.), attested from c. 1300 as "soft, flabby, flexible, pliable," but by 17c. meaning "puffed up, swollen." It is perhaps from a Scandinavian source akin to Old Norse blautr "soaked, soft from being cooked in liquid" (compare Swedish blöt fisk "soaked fish"), possibly from Proto-Germanic *blaut-, from PIE *bhleu- "to swell, well up," extended form of root *bhel- (2) "to blow, swell."
Influenced by or combined with Old English blawan "blow, puff." Figurative use by 1711. Intransitive meaning "to swell, to become swollen" is from 1735. Related: Bloated; bloating.