think of it in energy terms
as a first order approximation.
kinetic energy required to keep the rotor going round needs to come from somewhere when the motors stop (this value is pretty fixed regardless of aircraft mass or collective pitch)
KE =1/2xMxVxV where M is the rotor mass & V is rotor speed
an aircraft at height has potential energy
PE=MxGxH where M is aircraft mass, G is a fixed constant, H is height (so a heavy helicopter has at the same height more potential energy than a light one)
therefore converting aircraft potential energy (variable with mass) into rotational kinetic energy (fixed by rotor mass) requires a loss of height.
if the rotational power is fixed (ie rate of energy use) the rate of potential energy change is also fixed, so an aircaft with more mass must lose less height in a fixed time than a light one for the same energy conversion rate, ie a heavy aircraft will lose less height in the same time than a light one when in autorotation as can be demonstrated
This leads to the interesting (but patently nonsense) statement that an infinitley heavy aircraft can hover in autorotation (rate of descent becomes infinitley small at infinite mass)
DM