"subject (someone) to cruel horseplay," 1850, American English student slang, from earlier nautical sense of "harass with work, punish by keeping at unpleasant and unnecessary hard labor" (1840), perhaps from hawze "terrify, frighten, confound" (1670s), from French haser "irritate, annoy" (mid-15c.), which is 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." [Richard H. Dana, "Two Years before the Mast," 1840]
"opaqueness of the atmosphere," 1706, probably a back-formation of hazy (q.v.). Sense of "confusion, vagueness" is 1797. The 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; this may be an effect of the English climate on the English language.