"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.
late 15c., "symbol, emblem," from Latin typus "figure, image, form, kind," from Greek typos "a blow, dent, impression, mark, effect of a blow; figure in relief, image, statue; anything wrought of metal or stone; general form, character; outline, sketch," from root of typtein "to strike, beat," from PIE *tup-, variant of root *(s)teu- (1) "to push, stick, knock, beat" (see steep (adj.)).
Extended 1713 to printing blocks of metal or wood with letters or characters carved on their faces, usually in relief, adapted for use in letterpress printing. The meaning "general form or character of some kind, class" is attested in English by 1843, though the corresponding words had that sense in Latin and Greek. To be (someone's) type "be the sort of person that person is attracted to" is recorded from 1934.
The Old English verb is cognate with Old Norse stytta (assimilated from earlier *stynta) "to shorten, make short, tuck up;" and the modern sense of the English word might be from Old Norse or from an unrecorded Old English sense. Related to stunt (v.) and stutter (v.). Sense of "be careful in expenditure" is from 1848. Related: Stinted; stinting. The noun is attested from c. 1300.