This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / Monstrous Regiment
Jackrum's grand entrance: "His face was red, but his jacket was redder, and his sergeant's sash was a pure quill of redness, its very essence. The red of dying stars, and dying soldiers."
Shortly afterwards, from the Duchess: "You must invade Borogravia! In the name of sanity, you must go home! The winter is coming, the trusting animals are not fed, old men die of cold, women mourn, the country corrodes... you believed I watched over you, and listened to you ...and so I had to, I had to listen to you, knowing there was no help." The entire speech qualifies, but those are the highlights.
The bit where Polly is speculating about how Wazzer's religious mania got started. I don't remember the exact wording, but she imagines Wazzer being hideously abused at the Girl's Working School... "And then, one day, you'd look up into the only smile you ever saw..." Which would have been the ever-present painting of the Duchess.
Specifically, there's the part when Polly asks Wazzer what she used to do, and Wazzer replies, serenely, "I used to be beaten". Poor girl.
Tonker and Lofty have a bit of this as well.
A bit? Did you read Lofty's backstory? Just thinking about it makes you tear up...
Lofty: (sadly) I would like to eat chocolates in a great big room where the world is a different place.
Lofty's past is so awful that arson counts as heartwarming.
Tonker's dark, understated fury when she lays out exactly what was done, not to her, but to Lofty. "She was pregnant when she came back" says everything Polly needs to know.
Tonker, for all her lack of "middle gears" and generally abrasive nature, treats Lofty like glass. The fact that basic respect and kindness and love being shown to the poor girl is emotional enough to be a genuine tearjerker says a lot about the hell their lives used to be.
"Yes, a good swipe at head height would kill . . . some mother's son, some sister's brother, some lad who'd followed the drum for a shilling and his first new suit. If only she'd been trained, if only she'd had a few weeks stabbing straw men until she could believe that all men were made of straw "
Someone found Paul a box of colored chalks. You will cry.
...And Jackrum's grand exit. After letting Polly in on the fact that he's a she as well, and pointing out that his long-lost son probably doesn't want a fat, tobacco-chewing, swearing old woman turning up and claiming to be his mother, Polly points out they'd probably be thrilled to welcome a legendary and honoured sergeant to the family home. Jackrum later writes to show that he is indeed the benign and respected patriarch of his clan now. It's pretty rare that transgender identity is presented as a Happily Ever After.
Jackrum: Are you crying, Perks? Polly: Well... it's a bit sad, sarge. Jackrum: Oh, I dare say I sobbed a bit too, once in a while.
Relating to that, The Reveal that Jackrum's boyfriend William had a happy relationship with her, right up until he was killed in a battle at Sepple. Whilst he was standing right next to her.
The part where Polly remembers buying Paul a set of paints so he could paint birds, and how their mother had punished both of them for it, because pictures of living things (apart from the Duchess) are one of Nuggan's many Abominations.
It was a terrible thing. Her mother had been a kind woman, or as kind as a devout woman could be while trying to keep up with the whims of Nuggan, and she'd died slowly and painfully, amid the pictures of the Duchess and among the echoes of unanswered prayers, but that was the memory that crawled treacherously into Polly's mind every time: the fury and the scolding, while the little bird seemed to flutter in the flames.
The Fate Worse than Death of the Duchess. She died, but because the government refused to tell everyone that she was dead, people kept praying to her to intercede with Nuggan, and because Nuggan's Abominations were so insane, all the genuine belief went to the Duchess, elevating her to god (or god-like) status. But she didn't have much power- at least, not enough to actually help the people praying to her- so she had to keep hearing constant pleas for help that she couldn't actually do anything about. No wonder Wazzer kept hearing her crying.
The story about how Polly got the letter from Paul - a small group of soldiers were passing through Munz on their way home. Some had missing limbs or eyes, but a couple were essentially dead men walking. One of the soldiers had been carrying the letter from Paul, and once he'd given it to Polly, he died with little fanfare.
Apart from the letter and the medal, all the man left behind was a tin mug and, on the floor, a stain which wouldn’t scrub out.