How does gross weight affect helicopter autorotation?
If you look at the situation in terms of power, an increase in weight (or any increase in loading) requires more power. As you don't have this power, the helicopter will descend faster, more air will go through the rotor leading to an increase in RPM. Hopefully this increase in RPM will provide enough lift to stabilize the vertical speed. Increasing the pitch to maintain the RPM within limits provides lift in a slightly more efficient manner so the vertical speed will be slightly reduced (compared to the situation of descending with the collective flat down and RPM screaming over the limit)
That said, I find the affirmation in your book very confusing. Maybe I'm missing something, but a heavier helicopter will descend faster than a lighter one under the same conditions. It needs more power to fly and the only way to get it is to descend faster. That makes landing more dangerous, because you have more vertical speed to offset during the flare and more weight to cushion before touchdown. If increased weight and increased rotor loading would provide lower descent speed I guess everybody would autorotate in fully loaded helicopter and doing tight turns all the way to the ground :)