My senior design project had to do with weather balloons. Our design to have a balloon payload float at a goal altitude for an extended amount of time was a two-balloon system, where one balloon is released at the goal altitude to achieve neutral buoyancy, and the second balloon was released after an hour or so, dropping the payload back to Earth with a parachute.
It's possible to make a balloon neutrally buoyant at a specific altitude by calculating the pressure and tempertuare at your goal altitude using standard atmospheric models, but there are a couple of problems with it:
1) generally weather balloons are launched with excess helium to make them rise quickly through the jetstream and minimize drift in the wind. But, if a single balloon is filled to be buoyant at a specific altitude, it will have a very slow rise time. A balloon with the correct amount of helium for neutral buoyancy at altitude will only be very slightly positively buoyant at low altitude. This will tend to maximize float time in the jet stream as its rising, making the balloon fly very far away, out of range of radio receivers. Whatever is launched on the balloon will probably never be found again.
2) Helium leaks out of the baloons pretty fast. The balloons are thin latex, and helium is very diffusive, so the balloon might be neutrally buoyant for a while, but in a few hours begin to fall.
3) The temperature in the atmosphere drops until about 50 or 60,000 feet, and then begins rising again. Therefore it wouldn't really be possible to design a balloon to be neutrally buoyant higher than this temperature gradient unless you vent helium or use some other system to reduce/control buoyancy.
