A govt pamphlet on tires (Riding on Air) says, "To ensure proper handling, install the same type of tire on all four wheels"
The Michelin RV Tire Guide notes the 'corner weights' can be different, but , "for control of your RV, it is critical that the tire pressures be the same across the axle". so use the higher weight. They advocate some over-pressure per actual weight too, for shifting of load from side to side which is common in RVs so have some extra psi as a reserve for that temporary extra weight.
IMO there is also the tire tread designs where one might have a better grip so you could have a handling problem.