"having a sharp slope," Old English steap "high, lofty; deep; prominent, projecting," from Proto-Germanic *staupa- (source also of Old Frisian stap "high, lofty," Middle High German *stouf), from PIE *steup-, extended form of root *(s)teu- (1) "to push, stick, knock, beat," with derivations referring to projecting objects (source also of Greek typtein "to strike," typos "a blow, mold, die;" Sanskrit tup- "harm," tundate "pushes, stabs;" Gothic stautan "push;" Old Norse stuttr "short"). The sense of "precipitous" is from c. 1200. The slang sense "at a high price" is a U.S. coinage first attested 1856. Related: Steeply; steepness. The noun meaning "steep place" is from 1550s.
"to soak in a liquid," early 14c., of uncertain origin, originally in reference to barley or malt, probably cognate with Old Norse steypa "to pour out, throw" (perhaps from an unrecorded Old English cognate), from Proto-Germanic *staupijanan. Related: Steeped; steeping.