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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The negative weight is a function of bouyancy, and you can determine the mass by measuring the weight directly (which ends up negative) and then adding the weight of an equivalent volume of Air to that then apply the relavent gravitational constant to convert from weight to mass.
Alternately, you can compress a kniwn volume of helium into a non-elastic container (such as a steel tank) and measure how much the mass if the container changes.
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