Old English deop "having considerable extension downward," especially as measured from the top or surface, also figuratively, "profound, awful, mysterious; serious, solemn," from Proto-Germanic *deupaz (source also of 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 root *dheub- "deep, hollow" (source also of 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").
By early 14c. "extensive in any direction analogous to downward," as measured from the front. From late 14c. of sound, "low in pitch, grave," also of color, "intense." By c. 1200, of persons, "sagacious, of penetrating mind." From 1560s, of debt., etc., "closely involved, far advanced."
Deep pocket as figurative of wealth is from 1951. To go off the deep end "lose control of oneself" is slang recorded by 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)., hard to understand