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"bend forward," Old English stupian "to bow, bend" (cognate with Middle Dutch stupen "to bow, bend"), from Proto-Germanic *stup-, from PIE *(s)teu- (see steep (adj.)). Figurative sense of "condescend" is from 1570s. Sense of "swoop" is first recorded 1570s in falconry.
"raised open platform at the door of a house," 1755, American and Canadian, from Dutch stoep "flight of steps, doorstep, stoop," from Middle Dutch, from Proto-Germanic *stopo "step" (see step).