Mrs. Ellen Dean, called Nelly, feels a certain amount of guilt regarding Heathcliff because she did not like Heathcliff when they were young (she is only about three years older than him), and she neglected him. Later on, too, she feels some added guilt.
After Mr. Lowood arrives at Thrushcross Grange, where Nelly has long been the housekeeper, she begins her narrative about those for whom she has worked all her life. Nellie tells Lowood that after Mr. Earnshaw brought home Heathcliff,
They [Catherine and Hindley] entirely refused to have it in bed with them, or even in their room; and I had no more sense, so I put it on the landing of the stairs, hoping it might be gone on the morrow....Inquiries were made as to how it got there; I was obliged to confess, and in recompense for my cowardice and inhumanity was sent out of the house.
As she continues her narrative, Nelly mentions again acts of her neglect as she speaks of the time that all the children became ill with measles, and Heathcliff was long suffering while Catherine and Hindley whined and demanded attention.
....still I couldn’t dote on Heathcliff, and I wondered often what my master saw to admire so much in the sullen boy....
At this point, Nelly simply does not have any feeling for Heathcliff, and because of this, she feels some guilt. Later, in Chapter IX, when Catherine informs Nelly that she is going to marry Edgar Linton, she makes derogatory remarks about Heathcliff, saying that he is beneath her and it would degrade her to marry him. However, she adds that she loves Heathcliff and their souls are one and the same. But Nelly knows
[H]e had listened till he heard Catherine say it would degrade her to marry him, and then he stayed to hear no further.
So, Nellie feels guilt as she knows that she should have gone after Heathcliff and told him that Catherine confessed her love for him. Perhaps she could have averted Heathcliff's elaborate plan for revenge that exploited the next generation if she had told Heathcliff about Catherine's confession of love for him.
Nelly feels bad for Heathcliff, because although Mr. Earnshaw and Catherine love Heathcliff, Mrs. Earnshaw’s feelings are more neutral; it is Hindley who loathes Heathcliff and treats him horribly.
Nelly knows just as Heathcliff knows that the color of his skin and poor education hold him back from many of life's and love's opportunities (such as being with Catherine).
Nelly also knows Catherine’s true feelings toward Heathcliff; while Catherine loves him, she realizes she can’t be with him because of his social class, forcing Catherine to marry someone else in order to gain her husband’s social standing.
It is after Heathcliff returns from his three-year absence that Nelly decides to try to help Heathcliff because of Heathcliff’s situation (horrible treatment, lack of education, skin color, being in love with the girl he can’t have…). She feels guilty that she hadn’t taken a more active role in bringing peace among those living in the estate, especially between Heathcliff and Hindley. Nelly pretty much raised many of the children in the story, but it seems she may have neglected Heathcliff more than she realized, rather than trying to make him feel included or equal to everyone else.
What Heathcliff wants is for Nelly to refine him, make him a worthy man who is well-mannered and good, and so she takes on this task to help him and hopefully dispel some of her guilt.