Gunnm/Tear Jerker

Death of Yolg. Don't click on this if you haven't read that far.
Battle Angel Alita has a few Tear Jerker moments, but two stand out particularly sharply:
- The fifth volume of the original manga, at the conclusion of Alita's battle against Berserker-fied Zapan. Before the fight, a mob gathers to coerce - then later beg when Alita proves beyond their capabilities - her to give up her life to Zapan, which will stop him from rampaging through the Scrapyard. Though she knows she has little chance, she goes anyway, engaging Zapan in a brutal slugfest that she barely stops from becoming a total one-sided loss by sacrificing bits of her body to escape each time she is pinned. It ends with Alita, torn almost to pieces, shakily crawling to a sprig of sweet pea - a sprig she planted with Koyomi at the beginning of the volume, and seemingly dying. It was shown not to be exactly the case in the next volume - though very close - but it did bring forth tears.
- Hell, Zapan's backstory qualified as a Tear Jerker. He's a repentant Jerkass who had finally started to turn his life around and find happiness...and then unwillingly destroyed it in a fit of Unstoppable Rage.
- Then, the ninth volume of the Last Order storyline has its finale, when Caerula almost breaks down upon seeing how ruthless and bitter Arthur Farrell became in the years since her near-death. Apart from trying to make him see reason, however, she also visited to give him a gift: half of his fiancee Haruka's flute, which had been broken when Caerula's lover, Victor Byron, bit and ultimately killed her. While only minutes earlier he appeared as entirely a remorseless tyrant, his face immediately softens as he gently reaches into his coat...and pulls out the other half of the flute, which he had kept immaculately preserved. As he presses the halves together, he holds the completed flute to his head and murmurs "My Haruka..." It was a terribly humanizing moment, full of bittersweet thoughts of what might have been. Cue the waterworks.
When Alita after years of searching for Ido finally finds him... she learns he had willingly had his memory erased. He will never know who they were to each other, and how much she sacrificed to find him. This troper really did cry with her.
In the ninth volume of the original series, Alita is trapped in Desty Nova's Ouroboros program. She is forced to have to kill Ido... or so she assumes. The first time she handles it somewhat stoically. The next time, not so much. Her breakdown is very heartbreaking.