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. 
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