。
She married him for his family background.
Literal
She [topic-は] his [genitive-の] family-lineage [for-ために] him [with-と] married.
家柄 ('family lineage, social standing, background') captures something specific to Japanese (and other class-conscious) cultures: marriage decisions historically influenced by the family's social position, status, or reputation, beyond just personal compatibility. The と here is the comitative ('with') used with verbs of marriage, partnership, meeting. ~ために ('for the sake of') marks her motivation.