What is the upward force of an moving object?
The upward force of a moving object is known as "lift".
No. Weight is the perceived force due to gravity pulling down on an object. The force of gravity doesn't change due to an object's motion. The fact that an object seems "lighter" at the end of lifting it is because its upward momentum and the law of inertia causing the object to continue moving upward until the force of gravity stops the upward motion.
It depends entirely on the situation. If the object is resting, the upward and downward forces must be equal. On a planet, like Earth, this would make the normal force (upward) and gravitational force (downward) the same quantity. In outer space, it would simply be inertia. If the object is falling, the upward force is less than the downward force. If the object is rising, the upward force is greater than the downward force.