This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / Ginga Densetsu Weed
John's death. Specially when during his beating to death, his thoughts goes to Gin, and he apologizes for not being able to be with him again.
When Bat and Kite's lives were spared and you see them shed tears.
Jerome's death in the anime. Weed imagining him returning at the end of the final episode is a particularly cruel tease.
The death ofGB in the manga. GB dying in his godson's arms after giving his life to save him from the Hybrid Bear... it's pretty damn depressing, especially since it was just around that time when GB was beginning to get over his cowardice and realize his full potential. That poor sweet dog...
Teru's father's death.
When we see Hidetoshi from Ginga: Nagareboshi Gin shooting the dogs he believes to be Gin and even his former dog John as a result of the Ohu dogs being mistaken for killing people (when the real culprit is Kaibutsu).