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In this chapter, Miss Havisham is asking for forgiveness from Pip for having been a part of breaking his heart. She commiserates with him because her own heart had been so broken once. Pip immediately forgives, but believes her to have been much more of a disservice to herself and to Estella in her actions. She took away the light (both daylight and a spiritual sense of joy) from both their lives. In so doing, she destroyed a young girl's capacity to love, and she herself is growing old with none to love her.
Miss Havisham's request for forgiveness, of course, reminds Pip of his own need to reconcile and ask for forgiveness from Joe and Biddy and his treatment of them.
Reflecting the Christian influence in Victorian morality, those that do not seek reconciliation will sooner or later destroy themselves. We will see this in the upcoming chapters with Magwitch's hatred for Compeyson and Orlick's hatred for Pip.