A few points:
Weight on the tyres, for aircraft, is a variable even when the aircraft mass is constant. Hence the need for spoilers.
Well, whatever the arguments, F=uR always applies.
Hmm. But u is only constant for static friction. Once things are sliding everything gets way more complicated. Materials heat up / liquify / vaporise and this is where the big tyres make a diference.
iirc optimum slip for maximum antiskid braking is about 10% of velocity.