Must quadcopters have the same propeller sizes?
The main point of a quadcopter is that it can be controlled by engine power using much simpler fixed-pitch rotors¹. Assuming this construction, you need to be able to separately adjust power of


forward and rear set of propellers for pitch control,
left and right set of propellers for roll control and
clockwise and counterclockwise-rotating set of propeller for yaw control.


If you had two bigger and two smaller rotors, then one of the combinations would have the two bigger ones in one of the sets and the two smaller ones in the other. That would make it really, really hard to balance all the parameters to maintain appropriate controlability.

I think it might not be completely impossible, but it certainly makes no sense.



¹ Of course once you add cyclic and collective control, you can fly with one rotor only (well, two, or one with anti-torque rotor or jet) as most full-scale helicopters do, but then you've lost the simplicity of fixed propellers.