"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).
[1930+ Underworld; fr earlier sense ''decoy,'' fr the early 1800s practice of fastening pigeons and other birds to stools or stands as decoys; this term was applied to the decoy or ''hustler'' for a faro bank]
(also stoolie) A police informer; stool pigeon: He's nothing but a cop's stool (Underworld 1906+, variant 1924+)
: to make me stool on a friend (1911+)
[back formation fr stool pigeon]