Once again - the weight remains the same in high or low pressure therefore air pressure has no effect on weight.
The WEIGHT remains the same for the measuring scales if calibrated. The mass of the actual object would be the same to your view.
The reality would be that for you to pick up the object in both environments, the low pressure one would be easier to pick up, so would feel lighter, IF you could do it in that environment, which you can't.
The best way to give you an idea is to use the ground and a deep swimming pool. Get a piece of string and tie it around both bars. Pick one bar up off of the ground and feel the force it exerts against your pull.
Now drop one into the pool, then lift that out and you will find that the force to lift is, is greater, because it's under more pressure..
The thing is...when you place them aide by side, they weigh the same.