Origins
Before steep meant sharply angled, it meant impressively tall. Old English stēap described things that towered — cliffs, buildings, ambitious men. The emphasis was on height and prominence, not gradient.
The related word steeple makes the original sense clear. A steeple is etymologically 'a steep thing' — from Old English stēpel, something that rises high above its surroundings. Church steeples were the tallest structures in medieval towns, and the word captured their dramatic verticality.
The shift from 'tall' to 'sharply inclined' happened during Middle English. A tall cliff is usually a steep cliff; the two ideas overlap. Gradually the angle replaced the altitude as the word's primary meaning, and by the 15th century, steep described hillsides and staircases rather than towers.
Figurative Development
The figurative sense 'unreasonably high' (a steep price, steep demands) appeared in the 1850s. The metaphor is visceral: a steep price feels like a hill you cannot climb.
One common confusion deserves clearing up. The verb steep — as in steeping tea — is an entirely different word. It comes from Old Norse steypa, meaning 'to pour out' or 'to overturn'. The identical spelling is an accident of English's habit of absorbing words from multiple languages without marking their origins.