This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / The Wee Free Men
The story of what normal, decent people are capable of doing to an old lady when they suspect her of being a witch (kill her cat, burn her cottage, leave her to starve). Tiffany's reaction, even years later, is heartbreaking. Pratchett is a master at describing the banality of evil.
The Kelda's death. The Nac Mac Feegle who have so far shown themselves being tough as granite, free of worries and not caring too much when some of them died - as they believe they are the ones in paradise, and when one of them dies, they return to the world of the living - are grieving deeply as they lose their mother. It reminds Tiffany of the day she went to visit her grandmother and found her dead.
The hills had been quiet the day Granny Aching died. [...] Tiffany noticed the quietness. It was not the quietness of many little noises, but a dome of silence surrounding the hut. That was when she knew, even before she opened the door and found Granny on the bed.
The Drome in the Jolly Sailor dream, unexpectedly for a creature that had before that been depicted solely as predatory Paranoia Fuel.
"It thinks it's home, Tiffany thought. I've given it a dream it likes. [...] I wonder if it ever wakes up again."
When Tiffany defeats the Fairy Queen:
"I never cried for Granny because there was no need to," she said. "She has never left me!"
There's also the part where Granny Aching appears to Tiffany. Before she died, Tiffany had given her a little china statue of a shepherdess, but worried that it might be taken as an insult because her grandmother looked nothing like it. When she appears, Granny Aching is wearing the statue's outfit - a sign of how much it meant to her anyway.
The tragic tale of Miss Robinson, a poor orphan whose adult life was so lonely that she knitted a roomful of baby clothes and then kidnapped an infant boy, insisting he was hers.
Maybe even worse, her full name: Female Infant Robinson. Probably because her mother was a bit dense and thought "female infant" was the name of the child when the midwife wrote this down into her book, but the consequence is that Miss Robinson never got an actual name. She got just enough attention to be identified as female. After that, seemingly no one ever cared.
When Wentworth first goes missing, Tiffany immediately feels guilty for all the times she resented him.
It's your fault.
The thought felt like a piece of ice in her mind.
It’s your fault because you didn’t love him very much. He turned up and you weren’t the youngest anymore, and you had to have him trailing around after you, and you kept wishing, didn’t you, that he’d go away.
“That’s not true!” Tiffany whispered to herself. “I…quite liked him….”
Not very much, admittedly. Not all the time. He didn’t know how to play properly, and he never did what he was told. You thought it would be better if he did get lost.