Originally, to strike a person hard; nowadays, to shock, surprise, astonish, amaze, stun, or bewilder someone.
‘Knock for a loop’ which preceded ‘throw for a loop’ and might be related to ‘could have knocked me over with a feather.’ Google Ngrams shows ‘knocked for a loop’ appearing around 1918, and “thrown for a loop” around 1945.
Originally this American expression meant to render a person unconscious or, according to Wentworth & Flexner in the Dictionary of American Slang 1960, to make a strong, favorable impression.
‘Knocked for a loop’ was a sporting term, especially in boxing, as evidenced by this quote from The Wireless Age, August 1921, about the Dempsey-Carpentier heavyweight championship prize fight.
“Round after round, the fight goes on with continued reports of heavy punching, suddenly followed by a loud roar from the crowd. Father: ‘Listen! Somebody got knocked for a loop sure as guns!’”
This suggests that the original idea may have been a punch that was heavy enough to lay out an opponent by making him fall backwards and roll over. But other early uses show that it also had the sense of something that surprises or astonishes. Of course, if somebody knocked me ass over teakettle, I’d be very surprised!
Throwing somebody for a loop, on the other hand, doesn’t appear for about another decade and seems always to have had the idea of surprise behind it.
Several theories have been offered for the origin of the phrase. The American Heritage Dictionary of Idioms says that the ‘loop’ “alludes to the comic-strip image of a person pushed hard enough to roll over in the shape of a loop.” Cassell’s Dictionary of Slang attributes it to one “figuratively knocked ‘head-over-heels.’” Urdang’s Picturesque Expressions says that “The loop derives from the aeronautical term for the mid-air maneuver of an airplane,” or as we usually say, ‘looping the loop.’
Other possible sources are: a calf brought down by a lariat looped around a leg; or passengers looping the loop in an early roller coaster. The “loop” on roller coaster runs is the point where the coaster arcs upward through a complete circle, leaving passengers upside down at its apex.
Which is why I never ride roller coasters. Life hands me enough surprises, without searching them out.