Silas wants to keep the baby because he relates to her being alone and she reminds him of his little sister.
When Molly dies, she has her baby girl with her. Since the girl is only a toddler, she wanders into Silas’s house and falls asleep. Marner is standing at the door to hear the New Year’s bells, for good luck. His blurry vision hallucinates when he sees the girl.
[To] his blurred vision, it seemed as if there were gold on the floor in front of the hearth. Gold!—his own gold—brought back to him as mysteriously as it had been taken away! (ch 11, p. 61)
When Silas finds the baby, he decides to keep it. Godfrey goes to tell him to take it to the parish, and he asks why. Godfrey is surprised Silas wants to keep it because he is a bachelor and considered miserly.
“The mother's dead, and I reckon it's got no father; it's a lone thing and I'm a lone thing. My money's gone, I don't know where—and this is come from I don't know where. I know nothing—I'm partly mazed.” (ch 13, p. 65)
Symbolically, the child is gold. She brings new life back to Silas. He names her after his sister, and has a renewed interest in life that was taken from him since he lost his money. He wants to raise the child because she is alone as he is alone, and he needs someone to love.