In act 1, scene 1, when Rose comes outside, Troy puts his arm around her and says to Bono that when he met Rose, he "latched" on to her. He said to her he didn't wish to marry her, but "just [wanted to] be your man."
Rose responded by telling Troy she was looking for a husband, not a boyfriend, and that if he didn't want to marry her, he should get out of her way so she could find someone who would. Troy says he went away for two or three days to think about it, then came back after deciding to make her his wife. Rose says it only took him one evening to make up his mind.
While this is not the most romantic beginning to a marriage, it shows the practical side of both partners. As the stage directions tell us, the ten-years-younger Rose doesn't see a good option for herself other than marriage: she doesn't want a string of abusive relationships and babies out of wedlock, she doesn't want a life of partying, and she doesn't want to be alone. Troy is not a perfect human being, but he offers her stability: he also has a "fine" and "illuminating" spirit.