Old English feðer "a feather; a pen," in plural, "wings," from Proto-Germanic *fethro (source also of Old Saxon fethara, Old Norse fioþr, Swedish fjäder, Middle Dutch vedere, Dutch veder, Old High German fedara, German Feder), from PIE *pet-ra-, from root *pet- "to rush, to fly."
Feather-headed "silly" is from 1640s. Feather-duster attested by 1835. Figurative use of feather in (one's) cap attested by 1734. Birds of a feather "creatures of the same kind" is from 1580s; the same image is in Greek homopteros (variant birds of a beak is from c. 1600).
Old English fiðerian "to furnish with feathers or wings," from feðer (see feather (n.)). Meaning "to fit (an arrow) with feathers" is from early 13c.; that of "to deck, adorn, or provide with plumage" is from late 15c.
In reference to oars (later paddles, propellers, etc.), "to turn the blades in a horizontal position on lifting them from the water at the end of each stroke," to afford as little resistance as possible, it is attested from 1740, perhaps from the image of the blade turned edgewise, or from the spray of the water as it falls off (compare nautical feather-spray, that produced by the cutwater of a fast vessel). The noun in reference to this is from the verb. Meaning "to cut down to a thin edge" is from 1782, originally in woodworking. Phrase feather one's nest "enrich oneself" is from 1580s. Related: Feathered; feathering.