When Anastasia thinks that Dimitri is dead and cries over him only to discover that he was alive her reaction really sent this troper to heaven
Anastasia being reunited with her grandmother.
Also, when Anastasia explains to Sophie how did she escape from the Palace and mentions that a boy who worked in the kitchen saved her from the soldiers. This shocks Dimitri — because this he is that boy, and it's THE proof (aside of a certain key) that Anya is truly Anastasia. She can barely recall her early years, but she still remembers him even when she doesn't know that the man in front of her is the same boy who rescued her.
Dimitri's determination to prove Anya is the real Princess. Even though he'll lose the woman he loves and be seen as a kitchen boy again, he still does it. He's suffering because yes, he loves her.