I think I understand now why it says roll rate is function of angle of attack (during approach). It has to do with moment of inertia and dynamic pressure.
As you know, force is to mass and linear acceleration what moment is to moment of inertia and angular acceleration. Moments about points (or an axis) are created by forces. In this case we are dealing with rolling moments (about the longitudinal axis) created by the differential lift force in the ailerons.
On the one hand, for a constant speed, the less the weight, the less moment of inertia about the longitudinal axis, which means that the ailerons can create greater roll rates. This relation is inversely proportional.
On the other hand, for the same angle of attack (approach AoA) the less the weight the less the dynamic pressure. The less the dynamic pressure, the less the lift ailerons can create. This relation is directly proportional.
Both effects cancel each other and therefore roll rates due to aileron deflection will be constant for a given AoA regardless of the weight.