I try to explain it with a simple comparison:
Imagine something like a chewing-gum sticking to the road.
It is very lightweight but you already need a quite huge force to remove it from there (adhesion is dominating, friction coeff. is bigger than 1).
So now imagine you have a complete tire standing on the road. The adhesion force is still the same as on the chewing-gum but your tire and the car mounted to it is now much bigger. Adhesion force is not dominating anymore so your friction coefficient drops under 1.
The adhesion force is something you get "for free" you don’t need to put any weight on your rubber. So a light car will perform better because the relative amount of adhesion force is bigger even when the force itself is the same.
One thing you can do to increase adhesion force is to make contact area bigger.
If you zoom in on a side view of the surface of even a "smooth" material, it actually has many jagged points called asperities. As materials slide against each other, these asperities interact with each other. The actual frictional force can result from a variety of mechanisms such as: adhesion, abrasion, and hysteresis. As the load increases these asperities "mesh" together and the resulting energy dissipation due to the previously mentioned mechanisms increases, which causes the frictional force to increase. At some point the asperities are "fully meshed" (for lack of a better description) so the frictional force more or less peaks.
That’s an explanation of a physical point of view which we learn at school. The chemical force is not taken into account that’s why it can’t explain why a wider tire is better. It’s only true for rigid bodies but it is ok when you have a high load.
