what part does heathcliff play in Linton and Cathy's courtship?

Cathy came to talk to Nelly (neither of them knew Heathcliff was in the room, sitting behind the settle). Cathy said she was unhappy, that Edgar had asked her to marry him, and she had accepted. She asked Nelly what she should have answered. Nelly asked her if and why she loved Edgar; she said she did for a variety of material reasons: "he will be rich, and I shall like to be the greatest woman in the neighborhood, and I shall be proud of such a husband" (78). Nelly disapproved, and Cathy admitted that she was sure she was wrong: she had had a dream in which she went to heaven and was unhappy there because she missed Wuthering Heights. She said:

"I have no more business to marry Edgar Linton than I have to be in heaven; and if the wicked man in there had not brought Heathcliff so low, I shouldn't have thought of it. It would degrade me to marry Heathcliff, now; so he shall never know how I love him; and that, not because he's handsome, Nelly, but because he's more myself than I am. Whatever our souls are made of, his and mine are the same, and Linton's is as different as a moonbeam from lightening, or frost from fire." (81)

Heathcliff left after hearing that it would degrade her to marry him and did not hear Cathy's confession of love. Nelly told Cathy that Heathcliff would be deserted if she married Linton, and Cathy indignantly replied that she had no intention of deserting Heathcliff, but would use her influence to raise him up. Nelly said Edgar wouldn't like that, to which Cathy replied: "Every Linton on the face of the earth might melt into nothing, before I could consent to forsake Heathcliff!" (82)

Later that night it turned out that no one knew where Heathcliff was. Cathy went out in the storm looking for him, unsuccessfully––he had run away.