Clearly, the usual method of putting it on weighing scales won't work on earth because the balloon would float. I also don't think you could put it in a vacuum as, while the balloon wouldn't float, the vacuum would cause the balloon to expand and burst. (I think)
If there are a number of methods, which would be most accurate?
A few conditions
You can't weigh a deflated balloon and assume the mass of the helium is negligible.
No theoretical calculations of mass from data book values like density and atomic mass.
Helium makes the pitch of the voice rise, Sulphur Hexafluoride makes it go down. Ignoring the question 'Why would anyone want to?', is it possible to make a mixture of Oxygen (and possibly Nitrogen), Helium and Sulphur Hexafluoride so that when you breathe it in, your voice sounds exactly the same as if you had not? Has anyone done it?