What causes Nelly to finally agree to take a letter from Heathcliff to Catherine?

Nelly goes to visit Isabella, who was recently married to Heathcliff and is now living at Wuthering Heights. There, she runs into Heathcliff, who asks after Catherine's health. Nelly tells him that her illness has altered her for the worse and that she is restless and weak, not at all like her former self. She also asks him to stay away, for Catherine's sake. Nelly says Catherine is getting good and humane care from Linton.
This news throws Heathcliff into close to a frenzy, because he realizes Catherine must be desperately isolated and longing for him with all her soul. He uses threats and persistence to persuade Nelly to deliver a letter from him to Catherine. Nelly doesn't want to do it, but Heathcliff warns her that if she doesn't help him plan a visit, he will show up with pistols and do violence to anyone who stands in his way of seeing Catherine. He impresses on Nelly that she will be helping everyone if she gives Catherine the letter he has written her. Nelly⁠—who of course wants to look good⁠—says she says "no" fifty times. Then she states,

in the long run he forced me to an agreement. I engaged to carry a letter from him to my mistress; and should she consent, I promised to let him have intelligence of Linton’s next absence from home, when he might come, and get in as he was able: I wouldn’t be there, and my fellow-servants should be equally out of the way. Was it right or wrong? I fear it was wrong, though expedient. I thought I prevented another explosion by my compliance; and I thought, too, it might create a favourable crisis in Catherine’s mental illness . . .