Forget about centrifugal force--stick to an inertial frame.there is a centrifugal force. and there is anti centrifugal that rope has on mass and gravity force.
The only forces acting on the mass are: the rope tension (which acts at an angle) and the weight (which acts down).
Since it's going in a horizontal circle, its acceleration is towards the center (centripetal) and horizontal.
So what must be the net vertical force on the mass?