How does the engine capacity affect the air conditoner of a car?

Answer 1

It doesn't realy.

An average air conditioner only draws 8 HP on todays mid sized cars.

On larger SUVs, Limos, vans, large luxury cars the A/C capacity and size is increased due to the larger passenger compartment.
The A/C on those draw 12-17 HP depending on the application. However, with larger vehicles you need larger engines of course.
So in a nut shell, engine capacity does not directly affect tha size of the A/C.

Answer 2

As far as I am aware it doesn't. It may however affect the power loss of the engine when it is turned on.