The most famous example in the 1950s-1970s of a man from the American South 'courting' a teenage girl is of course the white rock'n'roller Jerry Lee Lewis, who married his first cousin Myra Gale in 1957, when he was 22 and she was 13.
To give some more specific context than 'the American South', Jerry Lee Lewis had come from Ferriday in the rural Louisiana area of Concordia Parish, on the Western side of the Mississippi River, with the state of Mississippi on the Eastern side. Concordia Parish was, by all accounts, a violent place with a long history of duels and violence (it also had a poor life expectancy for the slaves who in 1860 outnumbered white people in the parish 10 to 1). Ferriday as a town appeared in 1906 as a result of a train line terminal being put there to serve the wider Concordia Parish, and Rick Bragg quotes an earlier author as calling Ferriday 'not only a bad town...the baddest town', due to the prevalence of violence, brothels, saloons and gambling dens in Ferriday. Lewis's parents were poor farmers but they belonged to a particularly incestuous clan of families which included Lewis's mother's sister's husband, the richest man in Concordia - so while Lewis's upbringing was quite poor, he as a white man had opportunities and connections that the majority black population of Ferriday did not). To give a sense of the incestuousness, Jerry Lee Lewis was 'double first cousins' with another member of the clan in Ferriday, the televangelist Jimmy Swaggart.
In the context of Jerry Lee Lewis's milieu in Concordia Parish, him marrying Myra at the age of 13 was seen as rather unremarkable. Myra was the daughter of J.W. Brown (who was the son of Jerry Lee's father's sister), who he met in Memphis, Tennessee, where he was making his music career. In order to marry Myra, he needed to leave Tennessee and perform a little legal chicanery; he went to Mississippi with a woman who claimed that she was named Myra Gale Brown and twenty years old (while the actual Myra was at school in the seventh grade) on a legal document. With this issue now dealt with, he was free to marry Brown, which he did in DeSoto County in Mississippi.
According to Rick Bragg's biography of Lewis,
The legions who have condemned him for it, for romancing a thirteen-year-old girl, have painted a picture that had nothing to do with reality, he said. His own sister married at twelve. People celebrated it, because, as his mama said, the child knew her own mind. Marriage to a girl of thirteen or fourteen was routine in his family’s history, and had been for as long as anyone could remember. It might be offensive to some, to many, but it was what was.
J.W. Brown did claim that he wanted to kill Lewis for marrying his daughter, and travelled to Sun Records' recording studios with a pistol, though he was relatively easily dissuaded:
“Talk is what talk is, just a bunch of yapping,” says Jerry Lee. “I done what I wanted to do,” and for J. W. or anyone else to pretend to be shocked by that, to be caught flat-footed by his courtship of Myra, by the fact that it led to a wedding, is a revision of the way things were in those days, he believes.
According to Bragg, Brown also intended to file criminal charges against Jerry Lee, but the prosecutor he talked to talked him out of it. The Phillips brothers at Sun Records knew about the situation, but they also clearly knew that Jerry Lee Lewis was a wild one and their post-Elvis money train. Said Sam Phillips:
It was a devastating, unnecessary, stupid damn thing, but what could we do about it? I think Jerry’s innocence back then [in dealing with the press]. . . backfired. They scalped him. It turned out to be a very ghastly and deadly thing. So many people wanted to do in . . . rock and roll, and this is just what they were looking for. It should never have played a role of such significance in Jerry’s life.
Aware that Lewis marrying a 13-year-old was a terrible look, the Phillips brothers tried to dissuade Lewis from taking Myra with him to England on tour with him in early 1958. When Lewis did take Myra with him and the British press found out, it was the kind of tabloid front page news that unsurprisingly destroyed his career: ROCK STAR'S WIFE IS 15 AND IT'S HIS THIRD MARRIAGE. This was reported on in the US as well, and the American media effectively blacklisted him. According to Hellfire, "Dick Clark of the TV show Bandstand later recalled that 'in a very cowardly act I decided to hold off further bookings for Jerry Lee on the show, for which I've been sorry ever since'."
In my little mind, I couldn’t believe that they could not see that I was a grown woman. I was only 13, but people said I was more mature than Jerry. I was serious-minded, I was like, “We gotta take care of this and do this,” and he was like, “Where’s the piano?” That’s what he is, that’s what he’s about. And I really, truly wasn’t a typical teenager.
... When we went back home, the whole country was “Shame on you, bad boy.” The other thing we had back then was a hypocritical society. It was “Do as I say, not as I do—and if you get caught, we don’t even know you.” Also, a lot of people took good notes when it happened. Elvis didn’t marry a little 16-year-old girl, did he? Priscilla lived with his grandmother for, what, seven or eight years?
However, in a People magazine article from 1989, Myra was clearly less sanguine about the horrors of her marriage to Jerry Lee Lewis than she is in the Alan Light interview:
After more than a decade of marriage, she says, Jerry Lee’s mean streak was a mile wide and growing. Daughter Phoebe witnessed at least one of her mother’s beatings, and it upset her. Myra said. “Phoebe was in the middle of the fire during the turbulent years. She was always jumping in the middle and trying to make it all go away. Phoebe had to grow up fast.”
By 1969 Williams was constantly gulping tranquilizers to stave off nervous attacks that caused her face to erupt in patchlike shingles. One night, when Lewis called in from the road and began drunkenly berating her, Myra pulled a pearl-handled pistol from her nightstand and announced that she was going to blow her head off. She said Lewis just told her, “Put the phone close, so I can hear it go off.” At that moment she decided to leave him. “Something in me snapped,” Williams recalls. “I had reached a point. There was no more tolerating it and being miserable. It was either die or leave. If I was still married to Jerry, I’d probably be dead by now.
So we have a situation where getting married to a 13-year-old was of dubious legality in the South, but nonetheless, in rural areas without civilised society having a strong presence, it occurred. And blind eyes were turned to its occurrence, by relatives, by prosecutors, by record company people - Sam Phillips saying that 'it should never have played a role of such significance in Jerry’s life' is a particularly revealing quote, as is Dick Clark's; both imply that getting married to a 13-year-old was seen as atypical and improper but not necessarily the kind of thing that should be career ending. So there was a whole lotta shakin' of heads going on, but not a whole lot of caring that maybe a man who marries a 13-year-old might also end up physically and mentally abusing her to the point where she was contemplating suicide.
Sources:
Follow up question: were there similar trends across the rest of the United States at that time?