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I understand the principle of leverage, but isn't the weight of the car that is being stopped a much more overriding factor?
Yes, the Weight/Mass being stopped is the most important factor of all (force=mass x decelleration)
Also assuming a standard weight is being decellerated by the brake system, variations in rim/tyre sizes from a 13" (0.560m diameter tyre) to a 17" (0.670m) diameter tyre will give a braking effort reduction of 20%.
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Larger-diameter tires will usually give a flatter contact patch and improve braking.
Braking efficiency does not necessarily go hand in hand with more rubber on the road.
With the road surface area increase you get from the larger tyre, the best effect you will get is that there is less load being supported per unit area so the tyre will not wear as much all things being equal.
The actual cornering/braking grip does not depend on area alone, but on the mass per unit area of the tyre and the softness of the tyre compound. These factors determine how much the rubber is able to push into the road surface providing the friction that prevents slip.
For a constant brake setup and vehicle mass, a big hard tyre will be the worst performer and a small soft tyre the best performer (up to the point the rubber shears of the casing).
My 2 cents worth again