Early instances of 'loving on [someone]'
The phrase "loving on [someone]" appears to have arisen fairly recently. A Google Books search turns up an instance from 1914, but it is put in the mouth of a native speaker of Arabic, for whom English is something of a language adventure. From Lucille Van Slyke, "Glad Rags," in Pearson's Magazine (1914):
"Take, hard-hearted one!" she joked in easy Arabic, but let her voice trail into "Ameercan En'leesch." "I got a bounce tp-day." The soft flood of Leila's condolences she brushed aside with a wave of her cigarette. "It is as always," she scolded pettishly. "I do work like the wife of the devil but always the boss gets a loving on me. In Beirut—in Alexandria—in N'york! It is ever the same. The ones that would marry with me is cheap skates! The ones that would not—bah!" Her white teeth shut vindictively, she sprang up with a gesture of dismissal. "They is all fools. I, Miladeh Khouri——" she corrected herself naïvely, "Milly Kelly, I is not a cinch!"
The next match is from 44 years later in dialogue involving a rustic native U.S. English speaker, from a story in Ladies Home Journal (1948) [combined snippets]:
"Up to now, the babe had just laid in my arms a-looking at him. But when he leant forrerd, it all of a sudden raised up, with a little joyful cry, and grabbed at him—yes, actually wanting to leave me for him! He tuck it, and when it hugged his neck, busted out a-crying something awful behind its head, whilst I just sot there dumfoundered, watching at it loving on him."
The expression really began to pick up steam (in print sources included in the Google Books database) in the 1970s, perhaps influenced by versions of the expression "Lay a little loving on me." In the spring of 1973, Eddie Floyd (who may be best remembered for his original version of "Knock on Wood") released a single with the title "Lay Your Loving on Me" for Stax Records, and three years earlier Robin McNamara had released a single called "Lay a Little Loving on Me". In the August 22, 1970, issue of Billboard magazine, yet another similar song title is mentioned as a Best Pick in the country music category by the program director at KFAY radio in Fayetteville, Arkansas: David Wilkins's "Put a Little Loving on Me."
The "loving on" formulation also appears in James Whitehead, Joiner (1971), in a scene set in Hattiesburg, Mississippi:
"You from Texas?" and then there's the clatter of the little plate and sounds of furious lovemaking that cause me to imagine exploding hooks and eyes and also an extraordinary flak of girdle parts. For a moment I couldn't tell whether Fred was loving on her or beating her up for being from Texas and teasing him, but finally I satisfied myself it was only a fizgig and her fellow having fun.
The next verifiable match is from Bruce McGinnis, The Fence (1979), a novel set in north-central Texas [snippet view]:
...him when no one else could have just by being a little kinder with him and loving on him a little more, what any brother would do for any other brother. Just by loving the fear and confusion out of him and saved him. But I was too busy with Annie to notice, and besides it doesn't make any difference now anyway.
Another instance from the U.S. South appears in the case of Hester v. State of Mississippi (an appellate decision released by the Mississippi State Supreme Court on February 13, 1985, but citing testimony given at the criminal trial of the defendant one or two years earlier):
Ernie's waitress, Linda Pigg, stated that she saw Winn in the bar shortly before 4:00 p.m. and that a woman approached Winn and started talking and "loving on him". Ms. Pigg saw them leave about 4:00 p.m. About two hours later, Ms. Pigg saw the same woman return alone.
The common feature of these early instances of "loving on [someone]" is that they appear to be set in Southern U.S. locales such as Mississippi and Texas, and in dialogue spoken by not especially well-educated people. The religious angle in usage of "loving on [someone]"—mentioned by a couple of answerers here—is apparent in some instances from the past 25 years or so, but not in the earliest examples.
In any event "loving on [someone]" in its modern sense appears to be several decades older than "hating on [someone]," as detailed in the EL&U question (and answers) Origin of 'hating on'.