Does the size of your wheel affect your vehicle MPG? I figured if your draw a dot on a big wheel, it'd take longer to travel a full circle than if the dot was on a smaller wheel. Also, bigger tires on smaller wheels probably weigh more, right?
The diameter of the tire affects the cruising RPM of the engine.
Larger diameter tires will give better fuel economy, but will reduce your acceleration and power at low speeds. There is no free lunch.
Larger wheels also have less rolling resistance. This is why race bicycles have huge wheels.
The difference is so slight, that it's not worth playing with it and affecting all the other dynamics of your car. The way your car came from the factory is optimised for general use.
aluminum is twice as dense as rubber, but then you have to factor in torque and angular momentums....
Nobody does this. You're overthinking it. The best way to improve fuel economy is with your driving habits.
Larger tires will impact (decrease) fuel economy due to increased weight and rolling resistance.
Look at the chart in car&driver especially. The differences in economy are fractions of a mile. Hitting one red light makes more of a difference than your tire size.