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They were married for about two seconds, before Linton died.
Heathcliff forced Cathy Jr. to marry Linton in order to acquire Cathy Jr.'s inheritance from her father Edgar. As her husband, Linton would have complete control over this property. Heathcliff then has Linton write his will so that his father Heathcliff inherits everything.
After the marriage and the arrangement of the will, Linton promptly dies (he always was sickly) and his widow Cathy Jr. is basically left penniless. She stays on at Wuthering Heights, and falls in love with Hareton, and so on and so forth.