Yeah i understand forte, the 2nd half of FF6 really didn't have a whole lot of storyline writing, it was basically up to Setzer, then bits and pieces put together if you wanted to up to kefka
Actually it seems to be more about each individual character dealing with their past issues, and finding a way to cope with them (spoilers)
It starts out with Celes' loneliness issues, with her being standed with and having to protect the only parental figure she's ever known, and of course if you don't do the scenario correctly, Cid dies.
Sabin and Edgar don't really have much backstory in the World of Ruin, theirs was pretty much done with in World of Balance
Setzer has his past with Daryl of course, coming to terms with the death of an old co-pilot
Most of the rest are optional but still crucial to the story, like Cyan finally saying goodbye to his wife and child for good, Gau finding out his father abandoned him on the Veldt, Shadow's dreams about his former gang and their tragedies, Terra finally understanding what it means to be loved and needed, Locke trying to revive his dead fiance whose death he feels responsible.
Strago/Relm have that thing north of Themasa, but IIRC it was pretty useless and didn't offer anything story-wise.