This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / Now and Then, Here and There
As Grave of the Fireflies will teach you, war is not kind to children. Not even in a vast Crapsack World slowly dying in orbit around a star in the early stages of its own death. I (this is too important to be impersonal) suggest you set aside an entire day to watch it if you plan to. It's only 13 episodes long, but it can leave you unable to act for hours afterwords. And don't let the first episode fool you.
For this troper, it wasn't even a part of the series, but in the opening, at the realization that the photo of the carefree Sara, in her own world before the series starts, is the only time in the entire series she's shown smiling.
One episode's pre-title sequence. Abelia is woken up at an ungodly hour of the morning by Hamdo, has to listen to his rant and then get to work waking up Hellywood to do some complicated and unnecessary task. When she hangs up the phone, she sits and stares at nothing for a few seconds with a look of utter despair. Then she smacks herself in the face and gets out of bed with her usual expression, and the title credits roll.
Sara's story is a tear jerker from the beginning, when Shu sees her inside his cell and tries to talk to her, and she just jerks away from him without words like an abused dog. Going into the show knowing what she's been through actually makes it harder to watch.
The opening sequence of episode 6 was utterly brutal. Sara's near rape and escape into the desert is unspeakably difficult to watch. But the way she ran out of that building, tore off the soldier's uniform and stood free, her hair blowing in the wind, Taku Iwasaki's beautiful score playing, it's just too emotionally potent NOT to get teary-eyed.
When Shu and Sara meet again, she tells him "You lied to me." Sad not just because of her situation, but because of how Shu must feel knowing he let her down in a horrible way (even though there wasn't much he could've done).
Her attempt to kill herself after discovering she was pregnant was horribly depressing.
Sara deciding to not return to her own time/world, opting to raise her child in this new world. Was I the only one who felt incredibly saddened by this? Raaaaaah!
Elamba talks about his backstory, that the troops raided his village, killed people he knew, and took his sister he found her corpse half eaten by animals, and by this point, his tone shows that the experiences have taken a tole on his mind.
Even when he's dived head first into his campaign against Hamdo, the doctor, A Nice Guy and Sis's friend, tries to disuade him and telling him how far he's fallen. he shoots the old man dead.
There's something about how the show ends so abruptly, without any "epilogue" moments, staring up at the smokestacks as the credits roll.