1560s, "to move or walk in a stately manner," apparently from a dialectal survival of Old English swapan "to sweep, brandish, dash," from Proto-Germanic *swaip-, from PIE root *swei- (2) "to bend, turn" (see swivel (n.)). Meaning "pounce upon with a sweeping movement" first recorded 1630s (see swoop (n.)). Spelling with -oo- may have been influenced by Scottish and northern England dialectal soop "to sweep," from Old Norse sopa "to sweep." Related: Swooped; swooping.
1540s, "a blow, stroke," from swoop (v.). Meaning "the sudden pouncing of a rapacious bird on its prey" is 1605, from Shakespeare:
Oh, Hell-Kite! All? What, All my pretty Chickens, and their Damme, At one fell swoope? ["Macbeth," IV.iii.219]