I feel like this one's a really stupid and strange one to cry to, but out of the grimdark edge and the emotionally crippling things I've watched, Sora no Woto was the one that nearly brought me to tears.
If I had to describe the overarching themes of the story, it's about finding happiness in a world that seems to be in a perpetual decline. Though everything's going to shit, this squad of girls and the town they live in are managing to continue having fun, be it revelling in their cultural heritage or imaginary mafia shenanigans.
Spoiler Territory:
However, the scene that brought me to tears was one of the final moments of the show:
For context, two opposing armies are about to clash forces in the middle of this snowy tundra - considering their weaponry and armaments, most of them will probably die in the conflict. The squad girls in their spider tank are left at the sidelines devoid of any hope of saving these men's lives.
However, our cute main character decides to open up the hatch, stand atop the tank, and play 'Amazing Grace' as loudly and beautifully as can be. Note that throughout the show, she started from a shitty bugle player to a full-fledged military musician.
Thus, to this, the soldiers stopped at the sound of this distant trumpet, and they ceased all fire.
It was cliched as hell, and I totally saw it coming, but the sheer sense of Kanata's innocence in the middle of a near-bloody conflict turned me into a living crying man-baby-child.