"subject to cruel horseplay," 1850, American English student slang, from earlier nautical sense of "punish by keeping at unpleasant and unnecessary hard work" (1840), perhaps from hawze "terrify, frighten, confound" (1670s), from Middle French haser "irritate, annoy" (mid-15c.), of unknown origin. Related: Hazed; hazing.
All hands were called to "come up and see it rain," and kept on deck hour after hour in a drenching rain, standing round the deck so far apart as to prevent our talking with one another, with our tarpaulins and oil-cloth jackets on, picking old rope to pieces or laying up gaskets and robands. This was often done, too, when we were lying in port with two anchors down, and no necessity for more than one man on deck as a look-out. This is what is called "hazing" a crew, and "working their old iron up." [Dana, "Two Years before the Mast," 1842]
1706, probably a back-formation of hazy. Sense of "confusion, vagueness" is 1797. The English differentiation of haze, mist, fog (and other dialectal words) is unmatched in other tongues, where the same word generally covers all three and often "cloud" as well, and this may be seen as an effect of the English climate on the language.