The following assumes the tire diameter stays constant.
Inertia:
By modifying the wheel diameter, you will modify the total inertia of the wheel/tire assembly, thus affecting the acceleration of the vehicle.
It may increase or decrease, depending on the shape and design of the wheel. Here is a
calculator to get a crude evaluation for rotational inertia of wheel/tire.
Tire stiffness:
With a small wheel diameter, the vertical stiffness of the tire usually increases. This means that the tire radius will vary more under vertical load (such as weight transfer) (deflection = load / stiffness). This affects the force and speed measured at the contact patch (force = torque / radius; speed = rpm * radius).
The preceding is also true for braking, which will affect http://www.jakelatham.com/radical/info/brake_calculators.shtml.
Having a higher tire vertical stiffness also means that the tire can loose contact more easily with the road - if it is relatively too rough - hence affecting handling.
Similarly, the longitudinal stiffness will most likely decrease with smaller wheel diameter. This means that a very large acceleration/braking force can be absorbed, giving a smoother force transfer to the ground, like on drag tire for example:
Tire rigidity:
Having a smaller wheel diameter means a less rigid tire. This means that it is easier to remove the tire from the wheel under a lateral force, i.e. under lateral acceleration; A
beadlock is then necessary.
A more rigid tire usually also means lower rolling resistance.
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Also, as the wheel diameter increases (no matter the tire diameter), the force between the rim and the tire increases, which can lead to slipping; Again, a
beadlock may be necessary.
Finally, a larger wheel usually means more space for a larger brake system which can absorb more heat.