How does gross weight affect helicopter autorotation?

The factors which affect helicopter autorotational aerodynamics include airspeed, gross weight, rotor RPM, and density altitude. The effects of these factors can be examined during a few phases of the autorotation, including entry, steady state descent, flare, and touchdown. The effects of gross weight seem very unintuitive to me, so I would like clarification on how gross weight affects the steady state descent and the flare, in particular.

My helicopter aerodynamics book says the following:

Gross weight determines RPM at a given collective pitch. At high gross weight, more blade pitch is required to maintain a desired RPM, so higher gross weight results in a slower rate of descent, assuming all other variables remain the same.

So high gross weight decreases descent rate. That's unintuitive to me, so I'm trying to build a logical path. I know from experience that making tight turns during an auto causes RPM to increase. Tight turns increase positive Gs on the aircraft, which is equivalent to increasing weight. So higher gross weight will tend to increase RPM, requiring the pilot to raise the collective (blade pitch) to maintain RPM. There's question 1: why does increasing weight (or G loading) tend to increase rotor RPM?

The second logical step is how this required increase in blade pitch will decrease the rate of descent. I understand that increased blade pitch increases AOA, thus increasing the lift produced by the rotors. However, this increased lift is opposed by the increased weight that started this whole discussion. Here's question 2: for a given increase in weight, is the resulting increase in lift larger? This seems to be the only way to achieve a lower rate of descent.

Flare and Touchdown

My helicopter's flight manual includes the following diagram, titled "Minimum Height for Safe Landing after Engine Failure"

This chart indicates that at a given density altitude, it is unsafe to be too heavy during an auto. I assume that the danger is related to the flare and touchdown, since during the descent it seems safer to have a lower rate of descent. My intuition tells me something about how the rotors store energy as RPM during the descent, and the flare and touchdown dissipate that energy in order to slow the helicopter's forward and vertical speed. It seems intuitive that a heavier helicopter will require more energy to slow, which means at and above some threshold weight, the helicopter will not be able to flare enough to touch down gently. But, is there a more rigorous explanation for high gross weight being dangerous at the "bottom" of the autorotation, i.e. how energy is stored and dissipated in the rotors?