Nelly followed the children's relationship since they were very young. She was able to see the roughness in Heathcliff and the wildness in Catherine. As one who cares about a child, she was pleased when Catherine showed a more elegant and feminine side after her stay with the Linton. I think in the beginning she saw Catherine as playing a game with the two men.
Nelly probably wanted Catherine to be able to make a good marriage with Edgar, but she questioned Catherine about Heathcliff. It was when he had heard her asking Catherine if she would marry Edgar and what about Heathcliff, that he had overheard and left for the three years.
Catherine also had cared for Heathcliff and like a mother; she had watched him grow up. She was aware of his deep love for Catherine and his unhealthy moods. She took pity on him because of the way that Hindley had treated him. I believe she felt his torment and Catherine's as well. First she experienced Catherine’s agony in the Linton household and later Heathcliff's in his home. She must have yearned for them to find some degree of peace between them, but still felt sorry for anyone who had come in the middle of the two.