Why does a balloon weigh the same when empty as when filled with air at atmospheric pressure? Would the weights be the same if measured in a vacuum?

The inflated balloon filled with air at atmospheric pressure when placed in air will experience buoyant force which acts upwards. The volume of the air displaced by the inflated balloon is equal to the volume of the surrounding air displaced by the inflated balloon. This makes the weight gained by the inflated balloon due to the presence of air inside it to be compensated by the apparent loss of weight due to the buoyant force exerted by the air. Thus, the weight of the inflated balloon will be equal to the weight of the deflated balloon.
The weight of the inflated and deflated balloons will not be same when put in vacuum. It is due to the fact that there is no buoyant force which acts on the inflated balloon.
The weight of the inflated balloon will be equal to the sum of the weight of the balloon and air present in it. Thus, the weight of the inflated balloon is greater than the weight of the deflated balloon.