: I think that Balin decided to go to Moria as a result of Thorin's success at re-taking Erebor. Moria was the next objective on the 'Dwarven Hit-list'.

Balin was also one of Thorins company ( the oldest I think ), and thus a kind of hero. What would have been his social position if Thorin had survived the battle of five armies? After the death of Thorin, and Dains coronation, he might have defied Dain ( in a mild way ) and decided to make a move towards his own realm. Though I can imagine Dain would give his permission, because he beleived in Balin. ( It occurs to me that the dwarves are rather optimistic when it comes to their enemies, ex; Smaug, the Necomancer &c &c )
Later in LOTR he is even named king of Moria in the damaged book, Gandalf reads in the chamber of records in Moria.

Jan