Puff
Middle English: imitative of the sound of a breath, perhaps from Old English pyf (noun), pyffan (verb).
wiktionary
From Middle English puff, puf, from Old English pyf(“a blast of wind, puff”), imitative. Cognate with Middle Low German puf, pof.
From Middle English puffen, from Old English pyffan(“to breathe out, blow with the mouth”). Compare Dutch puffen, German Low German puffen, German puffen, Danish puffe, Swedish puffa.
etymonline
puff (n.)
c. 1200, puf, puffe, perhaps from Old English, pyf "short, quick blast of wind; act of puffing," from puff (v.). Meaning "type of light pastry" is recorded from late 14c.; that of "small pad of a downy or flossy texture for applying powder to skin or hair" is from 1650s.
From 1560s in the figurative sense of "empty or vain boast;" the meaning "flattery, inflated praise" is recorded from 1732. Derogatory use for "homosexual male" is recorded by 1902 (compare poof (n.2)).
puff (v.)
Old English pyffan, *puffian "to blow with the mouth," of imitative origin. Compare pouf, from French. Especially "to blow with quick, intermittent blasts" (early 14c.). Meaning "pant, breathe hard and fast" is from late 14c.
The meaning "to fill, inflate, or expand with breath or air" is by 1530s. The intransitive sense, in reference to small swellings and round protuberances, is by 1725. The transitive figurative sense of "exalt" is from 1530s; shading by early 18c. into the meaning "praise with self-interest, give undue or servile praise to." Related: Puffed; puffing.