What a gear ratio does is cause the engine to turn at a higher RPM at any given speed. More RPM equates to more Horsepower being transmitted to the wheels, at least up to the peak RPM in the HP curve.
Yes, it is true that the engine's capacity to produce power is not changed.
The engine will run about 300RPM faster at highway speed going from 3.73 to 4.10.
If you are happy with how it tows now, I agree with the others, 500lbs will not make a noticeable difference. HOWEVER, if the new trailer has significantly more frontal area than the old trailer, you may still need the gear change. Most of your power needs come from wind drag.