This is based on opinion. Please don't list it on a work's trope example list.
Tearjerker / My Mad Fat Diary
Tixie in It's a Wonderful Rae part 2 - Not only does Tixy fall ill in this episode, but one of her best lines is made even more sad when you learn that she eventually died.
Tixie: What? Did you think you could just slip out of the world with nothing happening because of it? Do you think anyone can do that?
Rae and Finn's breakup - Despite the fact that they are very much in love with each other, neither one of them can scale each other's issues. Finn has trouble expressing his thoughts so he can't assure Rae how much he admires her and cares for her in a way that she can understand. And Finn doesn't understand how deep Rae's issues go, so as much as he tries to be there for her he doesn't understand that the outside influences are making more noise that his love and affection. He honestly cares for Rae and thinks she's downright awesome, so he can't understand how down on herself she is because to him, she's perfect. It's a sad case of romantic love not being able to solve it all.
When Danny recalls when his mother died. He didn't understand when his father told him she wasn't coming back, and thought she was just at pottery class. He then breaks down while explaining he thought he'd see her come back again, her hands covered in clay.
Rae's last 'session' with Kester. She waits until their meeting to open up her A-level results. She gets enough points to go to Bristol University and Kester gives her one last hug.
Rae: See ya.
Kester: No, not if I see you first...
The last scene of the show in Series 3, with Rae on the train going to Bristol, imagining and seeing all the people who have helped her life in the window, including Tix.