Not A320 but my company had two MTOW for our B737, one certified for domestic operations and one for international operations. Same aircraft tails with no difference in tyre pressures or strut inflation.
The original operator (the one who did the tail specific aircraft specification from the manufacture) would have chosen the desired weights from the manufacturer catalogue, usually it is just a AFM supplement but others are equipment related such as engine power requested, undercarriage (heavy or light weight) etc.