From Old English 'blāwan,' PIE *bʰleh₁- (to blow, to swell) — cognate with Latin 'flāre,' source of 'inflate' and 'flavor.'
To produce a current of air; to move or be carried by the wind; to shape glass or produce sound by directing air.
From Proto-Indo-European *bhle- ("to blow, to swell with air"), via Proto-Germanic *bleaham ("to blow") and Old English blawan ("to blow, breathe, sound a wind instrument"). The PIE root *bhle- is widespread across Indo-European: Latin flare ("to blow" — note the initial fl- from bhl-), Greek phlein ("to abound"), and the Germanic family (Old English blawan, German blasen, Old Norse blasa). Old English blawan was a strong verb with past tense bleow (Modern English blew) and past participle blawen. The noun blast
English 'blow' and Latin 'flāre' (to blow) are cognates from the same PIE root — the difference is that Germanic languages kept the 'b' while Latin shifted it to 'f' (Grimm's Law in reverse: Latin 'f' often corresponds to Germanic 'b'). So 'blow' and 'inflate' are etymological cousins. Even 'flavor' comes from this root — via Latin 'flātus' (a blowing), because taste was associated with the breath or emanation of food.