The analyses of a text #2

The narrator recalls his childhood; he came home from the boarding school for his mother's sudden death.
Now all the funeral finished and when night came, Peggotty came to his room and tells him about his mother in her lifetime.
Peggotty is the only maid in his house.

.......................................
"She was never well," said Peggotty, "for a long time. She was uncertain in her mind, and not happy. When her baby was born, I thought at first she would get better, but she was more delicate, and sunk a little every day. She used to like to sit alone before her baby came, and then she cried, but afterwards she used to sing to it, so soft that I once thought, when I heard her, it was like a voice up in the air, that was rising away.
[David Copperfield by Charles Dickens]
I'd like to know if "it was" implied before "so soft that."
I think "that was rising away" is an object of "thought."
So I was wondering if "that" means "and that it."
Thank you in advance for your help.