My intuition leads me to believe that the balloon would have negative weight? and I have no idea how we could measure the mass
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Everything actually will weigh slightly less on a scale than it should when we weight it in an atmosphere. More dense objects will give you a more accurate weight. This is because everything in an atmosphere will experience a buoyant force proportional to its volume. The buoyant force is proportional to the weight of the volume of fluid displaced. F = ρgV, the density of the fluid, times gravity, times the volume of displaced fluid.
If we want to measure the mass of a balloon, we need to either remove the air around it, and weigh it in a vacuum. Or we could measure the volume of the balloon, calculate the buoyant force, and measure the net force on the balloon (by measuring how hard it pulls up) and then subtracting the buoyant force from that.
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