.......over non payment of fees for flying over their airspace. The news ticker says PIA hasn't paid the dues for last 6 months.

Anyone has a clue how much does it charge for flying over airspace of another country ? And how the rate is defined ? per hour or what ?

It varies. Some countries charge fees based on max landing weight, others by max take off weights, some by aircraft category and and some by distance traveled. For example, transiting US airspace will cost you $38.44/100nm and oceanic overflight will cost you $15.94/100nm

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