The two earliest matches for "hate on"/"hatin' on" that Elephind newspaper database searches turn up are from the same San Francisco Bay Area publication, in 1998 and 1999.
From Earl Vanbuskirk, Jr., "They Want It All: LOX," in the [Pittsburg, California] Los Medanos College Experience (February 27, 1998):
As for all of you that are still caught up in this East Coast/West Coast drama, let it rest in peace with Pac and Biggie. Stop hatin’ on Bad Boy and show love where love is due and give The LOX their props. After all it’s all music, right?
And from Keyairra Patterson, "United We Stand Divided We Fall," in the [Pittsburg, California] Los Medanos College Experience (November 6, 1999):
The problem here if you haven't noticed, there is no community unity or at least not enough and it is accompanied with two sicknesses which make it even worse. These sicknesses are hate and discrimination and whether you accept it or not, those are sicknesses. You may not agree with a lot of things people do or even say but that doesn't give you the right to hate them or hate on them. You may despise the things that people do or the way people live, but hate is a strong word and you really should be careful when you use it because it promotes bad carma.
The second instance quoted above is interesting because it indicates that—even at that early date—the writer sees a clear distinction between "hating" and "hating on." Regrettably, she doesn't spell out exactly what that distinction is.
Evidently, the expression was firmly in place in the Bay Area by the end of the 1990s. It is not at all clear, however, where the expression originated. Hugo's citations of USENET occurrences from 1996 indicate that there was plenty of time for the expression to have originated elsewhere in the United States and migrated to the Bay Area by 1998.