Old English deop "profound, awful, mysterious; serious, solemn; deepness, depth," deope (adv.), from Proto-Germanic *deupaz (cf. Old Saxon diop, Old Frisian diap, Dutch diep, Old High German tiof, German tief, Old Norse djupr, Danish dyb, Swedish djup, Gothic diups "deep"), from PIE *dheub- "deep, hollow" (cf. Lithuanian dubus "deep, hollow, Old Church Slavonic duno "bottom, foundation," Welsh dwfn "deep," Old Irish domun "world," via sense development from "bottom" to "foundation" to "earth" to "world").
Figurative senses were in Old English; extended 16c. to color, sound. Deep pocket "wealth" is from 1951. To go off the deep end "lose control of oneself" is slang first recorded 1921, probably in reference to the deep end of a swimming pool, where a person on the surface can no longer touch bottom. When 3-D films seemed destined to be the next wave and the biggest thing to hit cinema since talkies, they were known as deepies (1953).
Old English deop "deep water," especially the sea, from the source of deep (adj.).