Question

Will an empty balloon have precisely the same apparent weight on a scale as a balloon filled with air? Explain.

Answer 1

They would not, but only for this reason: In the the full balloon, slightly more molecules of air are pressing downwards on the same position. The difference lies in the weight of the volume of the inflated balloon that does not lie in space above the deflated balloon.
An air filled balloon is heavier than the empty one.

Answer 2

The notion an empty balloon have precisely the same apparent weight on a scale as a balloon filled with air depends on the diameter of the balloon. The weight of the balloon filled with air is equal to the mass of the balloon and the mass of the air inside. The mass of air inside is equal to the density of air multiplied by the volume of the balloon. If the balloon is large, then the two masses are equal whereas if not, the mass of air inside the inflation is neglible