Friction coefficient changes with load
If aircraft tyres are anything like automotive tyres, then you will find that the friction coefficient will reduce with increasing load. The tyre friction -v- normal loading will not be a straight line, but a curve.
Sorry to complicate your life.
BTW, this is the reason that lowering the CoG and widening the track of racing cars is beneficial as it more evenly distributes the load between the sides of the car during cornering, thereby increasing the total traction available.
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