What this suffix does
-wise comes from Old English "wīse" (manner, way). It converts nouns and adjectives into adverbs of manner.
likewise = in the same manner ("I will do likewise").
otherwise = in a different manner, or else.
clockwise = in the direction of clock hands.
crosswise = transversally, across.
streetwise = experienced in the ways of the street (adjective).
Contrariwise: Lewis Carroll's gift
In Through the Looking-Glass (1871), Tweedledee corrects Alice with "Contrariwise!" (= on the contrary, in the opposite manner). This word became iconic in English literature.
"contrariwise" = in a contrary manner, on the other hand. Used in elevated or ironic speech.
Other literary -wise words:
"nowise" = in no way, not at all (archaic/formal).
"sidewise" = sideways, to one side.
Modern -wise: informal expansion
In modern English, -wise became very productive in informal speech: "budget-wise" (as regards budget), "career-wise" (regarding career), "weather-wise" (as for the weather).
"How are we doing, budget-wise?" "Career-wise, this is a great move."
This pattern is now standard in educated speech despite older prescriptivist objections.