Nelly interrupts her narrative to tell Lockwood that her story has now taken them up to the previous winter. She and Lockwood then discuss the possibility of Cathy falling in love with him. Huh?!
Nelly resumes her narrative. Edgar presses her for information about his nephew, Linton, wanting to know if he is nearly as bad as his father. He confesses that he is ready to die and that he would be OK with Cathy marrying Linton if he wasn't such a "feeble tool to his father" (25.8).
Linton sends a letter to Edgar begging to see Cathy, but it's so well-written that Nelly figures Heathcliff actually wrote it.
Eventually Edgar consents to letting Cathy seeing Linton. He is clearly dying and would like for Cathy to live at Wuthering Heights, the home of her ancestors. He figures the only way to do that is by marrying her off to Linton. He has no idea that Linton is as sick as he is.
Heathcliff is getting worried, because to make his plan work, Cathy must marry Linton; that way he'll gets the Grange when his sickly son dies. So now he's in a race against Linton's death and Edgar's willingness to allow the marriage.