Increasing the Nr has two advantages for an increase in max gross weight. Firstly, increasing the speed of a rotating shaft decreases the torque, for the same power transmission.
Secondly, because the tail rotor is directly geared to the main rotor system, increasing its speed will also increase in proportion and reduce the blades angle of attack for the same thrust, making them less prone to stall at high pitch angles.
Obviously, increasing the Nr will result in a compromise elsewhere, such as bringing the aircraft closer to advancing blade speed problems in the high speed cruise.
The A109 series of helicopters are designed with a two position Nr switch. The Nr is set to 102% for flight below Vy and 100% above it. If the switch fails at 102%, the cruise speed has to be kept to 145kts or below.