The revelation of both Molly's death and the discovery of the child comes in Chapter 13. Silas offers little justification of his decision to keep the child, only blurting out that he feels he should keep her because it came to him, as if it were an act of fate or destiny that should bring them together. Note what he says in response to Mrs. Kimble asking for the girl:
"No--no--I can't part with it, I can't let it go," said Silas, abruptly. "It's come to me--I've a right to keep it."
The proposition to take the child from him had come to Silas quite unexpectedly, and his speech, uttered under a strong sudden impulse, was almost like a revelation to himself: a minute before, he had no distinct intention about the child.
Silas therefore seems just as surprised as everyone else his about his sudden decision to keep the child and his protestations that he has a "right" to keep her. Silas seems to find kinship with the little girl, however, saying that they are both "lone things." It is clear that Silas feels an irresistible compulsion to keep the child and that the girl has already gained his affections.
Silas is not quite in his right mind with all the events surrounding the finding of the child. He had just suffered another cataleptic fit, he was still in deep grief for the money loss, and his life had just shattered in front of his eyes.
Also, he had just realized that somewhere inside of him there is still room for some form of love when the child brought him wild childhood flashbacks.
So, when he brought up his justification for taking in the child, it is doubtful that he did that knowing what exactly he was saying, yet, he did mean it.
He said that he wanted to keep the child basically out of the dutiful sense of taking care of something other than his money. Perhaps, this way God or providence will look down upon him, bring him some mercy, and return his his gold. He did this for a three-fold reason: For the sake of sacrificing himself for something worth caring for, because the child did instill in him some sort of emotion, and because he really hoped somewhere in the back of his mind that if he did well with the child, his life and his gold will turn to him and everything will be normal.