1610s, of wind, "gusty," from puff + -y (2). Of other things, "swollen," from 1660s. Earliest attested use is figurative, "bombastic" (1590s). Related: Puffily; puffiness.
puffy tumid flesh
eyes with puffed (or puffy) lids
puffy off-shore winds
puff-adder
puff-ball
puffer
puffery
puffin
puffy
pug
pugilism
pugilist
pugnacious
pugnacity