Flannery O'Conner is not terribly clear as to why O.E. and Sarah marry in the short story, "Parker's Back."
Parker's comment about the marriage is ambiguous:
Parker understood why he had married her—he couldn't have got her any other way—but he couldn't understand why he stayed with her now.
We know that when he pretends to hurt himself fixing his car, she takes his hand and her touch goes through him like an electric shock:
Her own hand was dry and hot and rough and Parker felt himself jolted back to life by her touch.
This statement could infer that he has felt lifeless to this point—perhaps he feels dead inside and feels that this woman can bring him back to life: like a resurrection. O.E. does everything he can think of before they marry to please her. Afterwards, though, he wonders why he stays. If he isn't looking for salvation, perhaps his original attraction to her is simply a physical one.
It seems that the couple have little in common except for their poor, uneducated backgrounds. Extremely different from Parker, Sarah is a very religious. Maybe he simply represents something of a "bad boy" and she cannot quite resist to "flirt with the devil." For instance, he believes that while she says that she hates his tattoos, that she actually likes them.
He never met a woman who wasn't attracted to [his tattoos].
The attraction is a strange one. One critic suggests that perhaps Sarah marries O.E. in order to save him—and she seems to like him well enough before they wed. Perhaps O.E. needs her, sensing that she will bring him out of the loneliness in his life and lead him to salvation. And while Sarah may think she might be able to save his soul, she is not one to show him flexibility or compassion, berating him on multiple occasions for the things he does.
In either case, though there seem to be vaguely potential reasons why each has decided to marry the other, the relationship is not clearly based upon devotion to, or love for, one another.