Old English wis "learned, sagacious, cunning; sane; prudent, discreet; experienced; having the power of discerning and judging rightly," from Proto-Germanic *wissaz (source also of Old Saxon, Old Frisian wis, Old Norse viss, Dutch wijs, German weise "wise"), from past-participle adjective *wittos of PIE root *weid- "to see" (hence "to know"). Modern slang meaning "aware, cunning" first attested 1896. Related to the source of Old English witan "to know, wit."
A wise man has no extensive knowledge; He who has extensive knowledge is not a wise man. [Lao-tzu, "Tao te Ching," c. 550 B.C.E.]
Wise man was in Old English. Wise guy is attested from 1896, American English; wise-ass (n.) by 1966, American English (probably a literal sense is intended by the phrase in the 1607 comedy "Westward Hoe" by Dekker and Webster). Wisenheimer, with mock German or Yiddish surname suffix, first recorded 1904.
"way of proceeding, manner," Old English wise "way, fashion, custom, habit, manner; condition, state, circumstance," from Proto-Germanic *wison "appearance, form, manner" (see wise (adj.)). Compare Old Saxon wisa, Old Frisian wis, Danish vis, Middle Dutch wise, Dutch wijs, Old High German wisa, German Weise "way, manner." Most common in English now as a word-forming element (as in likewise, clockwise); the adverbial -wise has been used thus since Old English. For sense evolution from "to see" to "way of proceeding," compare cognate Greek eidos "form, shape, kind," also "course of action." Ground sense is "to see/know the way."
Old English wisean "make wise or knowing" (transitive), cognate with Old Frisian wisa, Old Saxon wisian, Middle Dutch wisen, Dutch wijzen, Old High German wisan, German weisen; from the source of wise (adj.). Intransitive wise up is attested by 1905.