"bend forward," Old English stupian "to bow, bend," from Proto-Germanic *stup- (source also of Middle Dutch stupen "to bow, bend," Norwegian stupa "fall, drop"), from PIE *(s)teu- (1) "to push, stick, knock, beat" (see steep (adj.)). Figurative sense of "condescend," especially expressing a lowering of the moral self, is from 1570s. Sense of "swoop" is first recorded 1570s in falconry. Related: Stooped; stooping. The noun meaning "an act of stooping" is from c. 1300. Stoop-shouldered attested from 1773.
"raised open platform at the entrance of a house," 1755, American and Canadian, from Dutch stoep "flight of steps, doorstep, threshold," from Middle Dutch, from Proto-Germanic *stap- "step" (see step (v.)).
This, unlike most of the words received [in American English] from the Dutch, has extended, in consequence of the uniform style of building that prevails throughout the country, beyond the bounds of New York State, as far as the backwoods of Canada. [Bartlett]
Also in South African English as stoep.