Weather deviation across the adjacent FIR

[Aceostrat]

Are there any limitations or adverse effects to deviate the weather into an adjacent FIR boundary. For example, you are on an oceanic RNP10 route like Culcutta FIR and you need to deviate more than 25 NM right of track which then put you into the boundary of Dhaka FIR.

Will Dhaka later charge an over-fly bill to your airline? or it's just free of charge in case of all kinds of contingency including weather deviations?

I really appreciate your replies.