Energy Terms
Dangermouse almost had it right.
It does come down to the energy equation. In autorotation the the power needed by the helicopter can only come from rate of change of potential energy i.e. Weight * Descent rate. The descent rate is therefore the power required (rotor profile power, induced power, power to overcome fuselage drag) divided by the aircraft weight. Hence the RoD decreases as weight increases. The helicopter would not hover if infinitely heavy, it just would not descend.