From Middle English steep, from Old English stēap (“high”), from Proto-Germanic *staupaz. Compare Old Frisian stāp, Dutch stoop (“grand; proud”), Middle High German stouf (“towering cliff, precipice”), Middle High German stief (“steep”)), from Proto-Indo-European *(s)tewb- (“to push, stick”). The Proto-Indo-European root (and related) has many and varied descendants, including English stub; compare also Scots stap (“to strike, to forcibly insert”).
The sense of “sharp slope” is attested circa 1200; the sense “expensive” is attested US 1856.
- Of a near-vertical gradient; of a slope, surface, curve, etc. that proceeds upward at an angle near vertical.
- a steep hill or mountain; a steep roof; a steep ascent; a steep barometric gradient
- (informal) expensive
- Twenty quid for a shave? That's a bit steep.
- (obsolete) Difficult to access; not easy reached; lofty; elevated; high.
- (Can we find and add a quotation of Chapman to this entry?)
- (of the rake of a ship's mast, or a car's windshield) resulting in a mast or windshield angle that strongly diverges from the perpendicular
- The steep rake of the windshield enhances the fast lines of the exterior. 
- (dialectal) brant
From Middle English stepen, from Old Norse steypa (“to make stoop, cast down, pour out, cast (metal)”), from Proto-Germanic *staupijaną (“to tumble, make tumble, plunge”), from Proto-Indo-European *(s)tewb- (“to push, hit”). Cognate with Danish støbe (“cast (metal)”), Norwegian støpe, støype, Swedish stöpa (“to found, cast (metal)”), Old English stūpian (“to stoop, bend the back, slope”). More at stoop.
- (transitive, intransitive) To soak an item (or to be soaked) in liquid in order to gradually add or remove components to or from the item
- They steep skins in a tanning solution to create leather.
- The tea is steeping.
- In refreshing dew to steep / The little, trembling flowers.
- (intransitive) To imbue with something.
- The learned of the nation were steeped in Latin.
- a town steeped in history