What happens to Nui Harime in Chapter 15 is arguably one of the most heartbreaking sequences in the entire story. Made even worse by the fact that she seemingly managed to conquer her demons and become an upstanding citizen many years ago prior to the beginning of the story.
The scene where Uzu Sanageyama breaks up with Ryuko Kiryuin in Chapter 12 is quite depressing since it's very clear that he still very much loves her at that very moment and all of the events that happens afterwards.
Satsuki Matoi's mercy kill and subsequent burial of the malnourished, mutilated girl inside A.K.I. is certainly one of the more sombre moments the protagonist of the story deals with.
Satsuki losing her ex-boyfriend Masanori to the Staple Eyed Gentleman in Chapter 20. Again, they may not have been dating anymore, but there was never bad blood between them. She was downright devastated by this loss. She's is equally upset by Izanami, said ex-boyfriend's fiancee, being brainwashed.
Even though she had been kind of a Jerkass, it is clear Ryuuko very much loves and misses her mother and wishes she could have stopped her from going after the OLF. It's also equally upsetting when we learn in Ch. 22, that she has resorted to Drowning Her Sorrows.
Satsuki feeling very depressed due to the past events and, naturally, it's equally saddening when she doesn't wear Junketsu anymore
Whether or not one would feel any sympathy for her, Ragyo's backstory in relation to her parents can be this. Her father, Gao, passed away when she was teenager, due to his experiments with the life fibers and her mother, Deitricha, lost a couple or a few of her limbs in said experiment, and, due to the life fiber prosthesis not syncing with her body properly, suffered routine staff infections (which aged her severely) until she died. Understandably, years later, she's still torn up about that.
In Chapter 28, while you still may not like Ragyo so much, its not hard to sympathize with her reactions when she sees what happened to Nui Prime. She, for a spell, shows a bit of humanity and hurries to her side, like any parent would their child.
