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Tear Jerker: 07-Ghost
07-Ghost has Mikage's death. Teito surely isn't the only one who can't stop crying after that * sob*
Teito's reactions and his suffering from PTSD and depression also count.
Ayanami's backstory is sad, despite being the main villain. He fell in love with the chief of heaven's daughter, despite not having anything thing like feelings, and her soul was reincarnated in order to prevent it from falling Veloren's hand. So until he could find it, he attempted to take all the souls on the planet to find her. It is sad, but cruel.
The Hausen House arc has many moments. Teito finds out about Castor'sor Xing-Lu's childhood... Since he was the Hausen's heir, one of the God Houses, he had a strict up-bringing... his father was cold to him and only his mother was allowed to be openly affective towards him... He was young but he had to protect the Raggs royalty and eliminate spies and traitors, he created dolls to ease his loneliness but was unable to smile or cry until he met and befriended Razette ;__;
From the same arc as above, the sad and desperating situation in which Castor's father finally showed how much he lovedhis son ... after being distant towards him for most of his life, he showed the depth of his paternal love and the measures he would take to protect his son... since, after siding with Raggs and losing the war they had to offer the head of their clan's leader as a token of peace to the Barsburg Kingdom.
"I want a love that would change my life"Castor's dearest wish... He only desired to live a simple life along with Razette...
When his father attempts to kill Razette(who changed her face to look like Castor's) so he could deliver her head instead to the Barsburg royalty (as they demanded after Raggs lost the war) Castor pulls an heroic sacrifice while thinking those exact same words
The chapter where Teito visits Mikage's family had this troper in tears. Goddamn, that was heartbreaking.