I mean, so many people in VI have tragic backstories and even many of their resolutions in the plot are pretty tear jerkers. Granted they all get better, but considering the sheer volume of drama that goes on, I kind of feel VI might have the most tragic cast of characters in the series.
Terra - Identity crisis and dealing with her inhuman heritage. Not to mention everyone wants to use her for her powers.
Celes - deals with being betrayed by people she trusted and caught in a love triangle with a woman in a coma. The death of her grandfather figure and the idea of the world being on the brink of death drives her to attempt suicide.
Locke - lost the love of his life, which left him guilt stricken, and can't get over her.
Edgar and Sabin - lost their father to the empire and grew estranged from each other with Sabin feeling that Edgar may resent him for turning his back on the family kingdom and their father's dying wish.
Gau was abandoned as a child and forced to grow up in the wild, his own father is a deranged man
Setzer - Lost a good friend and possible lover in an accident and has transformed himself into a reckless fatalist.
Cyan - Lost his home and his wife and child in a single night, even got to see them take a train to the land of the dead and felt angry at himself for not being able to save any of them.
Mog - May be the last moogle left in the world after the WoR.
Relm - lost both her parents when she was really young
Strago - taking care of the daughter of a friend who he knows but is sworn to secrecy not to divulge the identity of her father
Shadow - Betrayed his friend, left his wife and child because he was a fugitive, lost said wife, meets up with his daughter but cannot bring himself to reveal his identity, and most likely stayed behind to die as atonement for his crimes.
To top this all off, the world freaking ends halfway through the game and its partly the party's fault since they not only were manipulated into helping the Empire but then failed to stop the worst case scenario from happening.