One of the reason Balthier decided to leave Archades is because he couldn’t stand the madness and the obsession his father had with the stones. But then it was only research and studies. Now, he is facing the reality, that the research became real, and that other people become mad because of the stones. Here he examines the Judge’s body, the stone inside his flesh, and he is clearly disgusted.

Ashe decided to seek the sword and to destroy the Stone away before that, but Balthier kept quiet about the potential location of the Stone. I guess he waited for Ashe to actually get her hand on the sword first. 

This moment here in Bur Ominace, I think, is the moment he makes up his mind and he decides to get 100% involved. 

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