analogReference(INTERNAL) configuration
Changing the analog reference does not change the resolution.  All it does is change the measurement range. It compresses the existing resolution into a smaller voltage range.

If you then compress the voltage range of your signal in the same way to fit into the now compressed analog reference voltage range (for example by reducing the supply voltage to 1.1V) you end up achieving absolutely nothing.

The only time you would use the 1.1V internal reference is if your incoming signal is already between 0V and 1.1V and you would otherwise be wasting the resolution above the highest voltage the sensor gives out.