I cannot help with the direct history of this phrase, but the form seems similar to:
Pile on the hate
They keep on hating
In terms of prepositions, on seems to be only real candidate. I find all of the following awkward:
Stop hating at me
Stop hating to me
Stop hating by me
Stop hating up me
Stop hating with me
While you could suggest that the preposition is unneeded ("Stop hating me"), using hating this way changes the connotation from an emotion to an action. "Hating on" something is more akin to ranting or raging than simply stewing in invisible disgust.
As such, I wouldn't be surprised to find that this phrase has no common starting point or, if it does, it will be ridiculously difficult to find. Henry's answer regarding Shakespeare is a good example of how hard this will be to track down.
I found plenty of older uses using NGrams. Here are two from before 1900:
Well I knew The purport of his message, now declared; 'Tis such a one as foe might send to foe; The torture well becomes the Torturer! Then let him wreak his utmost hate on me, Loose all his stores of wrath; on me be thrown
The hit was in a review of Medwin's "Prometheus Bound" (translated from Aeschylus) which was first published in 1832.
The second was published in Frank Leslie's Pleasant Hours Volume 30. The book bears the date 1881.
You have looked scorn and hate on me often with these handsome eyes, you have railed at me often with these handsome lips, and now I will take righteous vengeance upon both.
However, both of these are much close to the idea that someone is piling on or actively causing hate to someone than "hating on" implies. But stepping from this to "hating on" seems reasonable.