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Tearjerker: Bake Monogatari
The end of the second episode, where Hitagi admits that she wonders if maybe she had given into the scammer cult's leader when he sexually assaulted her, her family would still be together. Ouch.
Also, earlier in the same episode, immediately after Hitagi has her weight returned to her. Watching her break down and cry after getting used to her stoic characterization can be quite jarring to the viewer.
In a severe case of Mood Whiplash, Koyomi goes from teasing Mayoi to nearly breaking down crying when he finds out that she's been Dead All Along and is in fact that lost cow, and the best way for him to get rid of her is to abandon her.
The last episode. When Araragi realizes that when Oshino told him "I'm going to leave this city one day", that in fact was his way of saying goodbye, because he doesn't like formally saying goodbye. Whilst we already know Oshino is a Jerk with a Heart of Gold, this shows that he is incredibly soft when it comes to goodbyes.
Episode 10 of the second season is a series of gut punches. 1) Alternate!Black Hanekawa killed Alternate!Koyomi. 2) Alternate!Kiss-Shot turns the entire town into zombies out of despair. 3) Oshino, Kaiki and Kagenui went off to face Kiss-Shot in what was most likely a Suicide Mission and are probably dead by the time Koyomi gets the letter he wrote and gave to Alternate!Mayoi. And then finally 4) Kiss-Shot herself shows up. It's just a generally depressing episode that thankfully ends happy. It's also kind of touching that in this world Araragi also ended up being with Hitagi.
The last episode of Shinobu Time, where Mayoi Hachikuji disappears for good.
It's strongly implied that Kaiki was not only beaten, but killed by his victimwhich does nothing to lighten the scene( he didn't actually die), and the season finishes off with an emotional Wham Line:
Kaiki: They say money talks even in hell. Since I don't have money saved up, I felt really glad from the bottom of my heart that I was able to earn some pocket change at the end.(In context, the "pocket change" is referencing good actions, i.e. helping people.)