A bigger battery will have a lower voltage drop for a given amperage. I would argue that the increase in voltage is what is causing the motor to spin faster. The motor is getting more watts, I guess it really doesn't matter if that is from an increase in voltage or and increase in amps.
I'm in Henderson and if you ever want to see what the amps are for the 7Ah and 5Ah batteries let me know. I have a meter that can read what the motor is pulling, takes about 10 minutes to do, 9 of those switching the battery.