Crab,
While a heavier aircraft does displace more air in a hover than a lighter one, this does not imply a higher downwash speed. The rotor diameter can be increased, hence resulting in more air being displaced for the same downwash.
Imagine two rotorcraft of the same weight, but one has a rotor diameter of 1 mile, while the other has a diameter of 1 inch. The downwash for the 1 mile rotor would barely be perceptible, while the 1 inch rotor will essentially be a rocket.