Lyddie is sad that her family is separated and she has lost the farm.
The phrase “leaden with sadness” means that you feel so sad that it weighs you down. It is a figure of speech. Lyddie is upset because she has returned to her farm, where she runs into a runaway slave named Ezekial. She feels bad for him and lends him money. When he says he will quickly pay it back, she sadly tells him there is no rush. What use has she for money? It won't get her family back together.
"Will you think of it as a loan, then?" he asked. "When I get established, I'll send it to you care of the Stevenses. With interest, if I can."
"There's no hurry. Wait till your family comes. I don't know when my brother and I can ever get back." She felt leaden with sadness. (Ch. 6)
Lyddie feels the separation of her family dearly. She tried very hard to take care of them. When her mother gave up, she let out the family farm to pay off her husband’s debts. He had gone west and was never heard from again. She also hired her children out. Charlie went to work for a mill, and Lyddie at a tavern.
Being back at the farm is hard for Lyddie. She is taking a short break from the tavern, and she has visited her brother. At the farm, she is just reminded of everything she has lost. Lyddie is an independent and strong-willed young lady, and she does not like feeling trapped.
"I hope you find your freedom as well, Miss Lydia," he said. It wasn't until she was well down the road that she began to try to figure out what he had meant. And he was right. At Cutler's, despite Triphena's friendship, she was no more than a slave. (Ch. 6)
Lyddie is freed from the factory soon after, however. She is fired for being away from the tavern. She feels this is unfair, since Triphena gave her permission. Mrs. Cutler doesn’t see it that way, though. Lyddie makes the most of it, deciding to take her fate into her own hands and get a job in a factory.