HZ39
Yes, the moment of inertia is proportional to mass... And to distance from rotation axis squared, too. All other factors constant, a weight reduction means a reduced moment of inertia. Moreover, fuel burn tends to redistribute weight towards the longitudinal axis, further reducing moment of inertia.
As the wings roll, other forces appear that finally cancel the moment and a steady roll rate is reached. I don't know those roll opposing forces in detail, but seems like they depend exclusively on the roll rate itself, like Drag depends on the airplane's airspeed. Therefore maximum roll rate should be constant regardless of airplane's mass. Moment of inertia would only affect the time to achieve that maximum roll rate. Am I right?