TL;DR
Now that I've had my coffee, I'll mention the problem with using a balloon in this sort of thought-experiment is any real balloon exerts some pressure on the gas (i.e. the gas is held in by more than just atmospheric pressure). That's why when teaching thermodynamics of gases problems start with "a frictionless piston filled with an an ideal gas". The container itself should not apply any forces on the gas.
OBTW, your weather balloon heading to the stratosphere will also experience a drop in temperature, which will work in the opposite direction as the decreased pressure.
But, absent a balloon, your Helium gas would continue to expand "forever" to an "infinite" volume. Unless you start to consider the very weak, but non-zero, forces of attraction between the He atoms ("London Dispersion Forces") and gravity.
Now that I've had my coffee, I'll mention the problem with using a balloon in this sort of thought-experiment is any real balloon exerts some pressure on the gas (i.e. the gas is held in by more than just atmospheric pressure). That's why when teaching thermodynamics of gases problems start with "a frictionless piston filled with an an ideal gas". The container itself should not apply any forces on the gas.
OBTW, your weather balloon heading to the stratosphere will also experience a drop in temperature, which will work in the opposite direction as the decreased pressure.
But, absent a balloon, your Helium gas would continue to expand "forever" to an "infinite" volume. Unless you start to consider the very weak, but non-zero, forces of attraction between the He atoms ("London Dispersion Forces") and gravity.