In fact a large fuselage hanging down from below the rotor can cause a helicopter to become unstable. If the helicopter rolls, the rotor will slip sideways, gaining horizontal speed. The drag on the fuselage below the rotor will cause the helicopter to roll further, causing increased slip and increased horizontal speed, hences increased roll. To avoid this the rotors will have dihedral (they're angled upwards slightly). This is what gives stability.
In fact a large fuselage hanging down from below the rotor can cause a helicopter to become unstable. If the helicopter rolls, the rotor will slip sideways, gaining horizontal speed. The drag on the fuselage below the rotor will cause the helicopter to roll further, causing increased slip and increased horizontal speed, hences increased roll. To avoid this the rotors will have dihedral (they're angled upwards slightly). This is what gives stability.
Somewhat counterintuitively, a helicopter is actually more stable in roll if the fuselage is above the rotor, but that usually makes it hard to land safely: https://books.google.co.uk/books?id=Q27ho2szWCoC&pg=PA346#v=...