My love for Linton is like the foliage in the woods: time will change it, I'm well aware, as winter changes the trees. My love for Heathcliff resembles the eternal rocks beneath: a source of little visible delight, but necessary. Nelly, I am Heathcliff! He's always, always in my mind: not as a pleasure, any more than I am always a pleasure to myself, but as my own being. So don't talk of our separation again: it is impracticable. (9.101)
To Catherine, she and Heathcliff are one and the same; thus marriage to Edgar does not mean leaving the man she really loves. That Heathcliff sees her marriage as a betrayal is what ultimately divides them.