The weight does not get 'lighter' as you lift it faster, and the argument put forth (which is getting more convoluted and less correct) is not only a poor analogy of how weight works, but also incorrect. The force that you exhibit on a set of scales (which at rest is purely m*G) is your weight. Jumping up and down does not decrease or increase your weight, but increases the force that is exhibited as a result of the velocity and direction of movement of the mass. This change in force is not a change in weight of the object, but purely a positive or negative force which changed the apparent weight that you must move.
With respect to the lifts, it doesn't change the weight of the barbell, but does change the force required to move/stop it.