1610s, of wind, "gusty, coming in puffs," from puff + -y (2). Of other things, "swollen," as if with air or some soft substance, by 1660s. The earliest attested use is figurative, "bombastic" (1590s). Related: Puffily; puffiness.
puffy tumid flesh
eyes with puffed (or puffy) lids
puffy off-shore winds