This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / Arata Kangatari
Nagu's past. He and his sister were abandoned by their parents, left to wander the desert in search of them. Sadly, his sister died before he gained control of his Hayagami. He later used it to resurrect her as a drawing and give them friends and a home.
Yorunami only ever wanted to reach his mother's expectations, but he could never meet them before she passed on. Then it turned out that she was only tough on him because she knew that his destiny as a shou would mean a very dangerous, difficult life.]]
Suguru's death. Harunawa says that he'll spare him if he agrees to say that he doesn't care about Hinohara, but Suguru refuses.
Kikitsune was originally a famous musician from Pompeii. Yes, thatPompeii. However, a jealous musician sent a slave to attack him, and the attack cost him his hearing. He got his revenge, but wound up pegged for murder.
Kagura's eternal youth. He found his Hayagami as a child, so he was forever cursed to never be able to grow up.
Also, it turns out that he was an amnesiac unable to remember his life before obtaining his Hayagami. This hits his only living family, Eto, really hard. And Kagura only remembers this right after Kadowaki forcefully absorbs Eto.
And then, as Eto has been almost entirely been absorbed by Kadowaki, Kugura remembers everything - and reaches out to Eto, crying out for his 'nii-san'. And Eto - he just smiles. He doesn't even care that he's being absorbed by Orochi, all he cares about is that his little brother finally remembers him, after three hundred years of being alone.
Yataka was in love with Himeou, but her role in society always kept them apart.
Both Yataka and Himeou were completely willing to elope, even if it meant that Yataka would have to forfeit both his territory and his Hayagami if they were caught (which we find out later is practically a death sentence to the sho) - and he didn't care. But on the day they were supposed to elope, Himeou vanished, returned to the palace, and afterwards would never speak privately to Yataka, and always treated him indifferently. He thought that she had just been using him, and we see him breaking the engagement necklace he had intended to give her. He spent fifty years stewing in rage and anger and betrayal, and he was the one to give the other shinsho the idea of assassinating her. It's only when Hinohara shows up that he learns that Himeou did truly love him, but on the day they were supposed to elope, she checked on the Hayagami for one last time - and found out that because she had neglected her duties as the ruler, a sho in the north went on a rampage and murdered everyone in his territory. She realizes that, even if she does love Yataka, she has to continue being the princess, and leaves Yataka.
After we discover that Yataka was in love with the princess, Kannagi guesses that if the assassination had been successful, Yataka would have killed himself in anguish. And he was right.
Yataka's anguished pleading that Hinohara save Kikuri.
The flashback Arata has of Harunawa murdering his parents.
Arata and Co. eventually come across a man from Japan who's been stuck on Amawakuni for fifty years. He wound up traveling between the two worlds right before he was going to get married, too. And since the person he switched places with died, he can never go back.
Isora was once a kind and happy noble in Inquisition-era Spain who was betrayed by one of his friends, whom he'd saved from being burnt as a witch. The Bishop in charge of the Inquisition convinced his friend to throw Isora under the bus so he could get his inheritance. He was then tortured until he sold out his entire family to end the pain. Before being sentenced to the stake, his tongue was ripped out using a hot iron and he was thrown into a river. When he came out of the water, he was in Amawakuni.
Yataka's reaction to Kikutsune obliterating his Zokusho, Okima and Aoi, with soundwaves is prettyupsetting. Made even sadder when Kannagi looks absolutely furious and gives Kikutsune a Death Glare, and we remember that all of his Zokusho and their families (including an unborn baby) were all forced to submit or killed (respectively) by Akachi pretty early on in the story, so he knows exactly how Yataka is feeling.
Rami's death, and Mikusa's reaction to it.
Kannagi, Akachi and Emisu's past together. Kannagi was originally from Haniyasu, Akachi's territory in the present, and was the son of a Lord. He meets Akachi and Emisu when they're being sold as child slaves, and they are both bought by his father, supposedly. The three of them grow up as friends, with Kannagi eventually growing feelings for Emisu. Akachi even teaches Kannagi how to fight! And then one day, Akachi tells Kannagi that he doesn't feel any loyalty to Kannagi's father for buying them, and says that he's glad Kannagi became his friend and treated him as an equal - only for Kannagi to admit that he was actually the one to buy the two of them, and that he's their real master. The look on both of their faces is just heart wrenching.
Right after this is a slave revolt, during which Kannagi's father is killed. Kannagi frees both Akachi and Emisu, and they manage to escape - only for the slaves to corner the three of them. Akachi saves Kannagi and Emisu by pushing them into an elevator-like machine that will take them to the sea and let them escape. You can even see Kannagi crying a bit as he's holding Emisu back. Kannagi even admits that he always dreamed of going back to save Akachi, but he was never able to.
The Final Battle between Akachi and Kannagi. Especially the ending, when Akachi reveals that he's been dead for more than a hundred years. Akachi collapses into Kannagi's arms and asks him to let Homura's flames consume him, and apologizes for everything he's done - and then submits to Kannagi, who refuses to let go of him until the fire has completely cremated Akachi's body. And then Kannagi goes back to Akachi's palace and tells Child!Emisu that Akachi is dead. What's her response? To tell Kannagi that Akachi was always telling her that Kannagi would take care of her when he and Akachi fought and Akachi didn't come back.
Akachi: If we fight, and I don't come back, don't be sad. At that time, Kannagi will come to meet you.
There's one scene at the beginning of the story, when Hinohara is being taken to his trial for the murder of the Princess. He briefly talks to Arata, who is in the real world, and just as the connection between them is ending, Hinohara hears his mom calling for Arata (who she thinks is Hinohara) in the real world, and all Hinohara can do is call out to her as the connection finally ends - and she's not even aware that her real son is in a completely different universe. Even though later on Hinohara becomes stronger and a lot more confident in himself, at that moment he's just a scared kid who needs his mom.