That is basically the Newtonian explanation, with "curvature of space-time" randomly thrown in. In General Relativity there is no "gravitational force", that opposes the force of the hand. That's why the ball experiences proper-acceleration upwards, when held in the hand.The reason you don't have to give the ball a push is because it already has a pushing force (gravitational force) acting on it due the curvature of space-time (this is what gives it weight). However, your hand is applying an equal and opposite force upward on the ball that prevents it from falling.
That is again the Newtonian explanation. In General Relativity there is no force acting in free fall. That why the ball experiences zero proper-acceleration when falling.Once you remove your hand from under the ball, the ball accelerates downward in accordance with F=ma.