Well lets see. Let us say you inflate the balloon at the surface where the pressure is 1 bar (10⁵ Pa). Now in the balloon, the pressure of the gas is slightly greater than one bar because the strength of the elastic balloon. The pressure of the gas inside is slightly greater than 1 bar. This is obvious since if we pop the balloon it goes pop... and a pressure wave is sent out POP!!). Now we allow this balloon to rise. Let us first assume the atmosphere is isothermal. as the balloon rises it encounters ambient atmosphere at lower pressure... now since the now the equation of state says that pV=mRT... where p is pressure, V is the volume of the balloon, m is the mass of gas in the balloon (constant) and R is universal gas constant divided by mean molar wt of air (about 28 g/mol) and T is thermodynamic temperature (T in Kelvin; T=273 +t (in deg C).

So as the balloon rises to lower pressure environment, the volume of the balloon will EXPAND so that pV stays constant as it must for an isothermal atmosphere.

So I think the balloon will expand... at some point when the skin thickness reaches a critical value (as balloon expands the thickness of balloon skin decreases) it will burst because the pressure of the gas inside will exceed the strength of the elastic balloon material.

P.S. The ideal gas law I have used has been written in form to explicitly consider the mass ,m in the balloon since that is constant. And one can see how the product pV must also there fore remain constant.

Consider a helium balloon that is filled at sea level. At sea level, the external atmospheric pressure of the air is equal to 14.7 lbs/in² or 1.0135 bar or 1 atm (those three values are all equal just like 1 yard is equal to 0.9144 meters). Since the balloon's volume is not changing, we know that the outside pressure on the balloon is balanced by the air pressure of the air inside the balloon. Another way of saying this is that the external and internal pressure forces are balancing.

Now release the balloon. The outside air pressure decreases as the balloon floats higher up in the air (assuming stagnant air and constant temperature). This can be explained by the following example: when you're swimming from the bottom of a pool up to the surface the water pressure decreases when you get to the surface of the water. Stagnant water pressure is caused by the weight of the water from above pushing down on you. Back to the balloon example, at sea level, the weight of the air in the atmosphere is pushing on the balloon. The higher up the balloon goes the less air there is to push down on the balloon so the pressure decreases.

When the balloon is really high, there is less air above the balloon than there was at sea level - so the weight of the air above the balloon is less than at sea level. The outside air pressure is pushing on the balloon less than it was when the balloon was at sea level. Therefore, the balloon will expand since there is less pressure being applied on it. So, the balloon should expand the higher up it floats in the atmosphere.

Now, consider taking an empty balloon really high up in the atmosphere and filling it up with air. Would its volume increase or decrease as you brought it back down to sea level?

Hint: The same thing would happen if you took an empty water bottle (that is filled with air), put its cap on, and brought it to the bottom of a deep pool. The volume of a water bottle filled with air would _______ as it was brought down to the bottom of the pool.

When a balloon goes up higher in the air, its size will increase. Since there's less air in the upper atmosphere, there's less stuff pushing back on the balloon, and hence the pressure is lower, which allows the balloon to expand.

If the balloon is flexible, then it expands as it rises to altitudes with lower air pressure. That's why weather balloons are released only partly filled, to prevent them from popping. I once had a bag of potato chips pop for the same reason: I bought them in Iowa (low elevation) and drove over a mountain pass in the Rockies.

The formula for understanding this is:
P*V = n*R*T
where P is pressure, V is volume, T is temperature, and n is the number of molecules of gas you're keeping track of. So...If the temperature is constant, if pressure goes down, volume will go up (balloon expands).If T is constant, and the pressure goes up (say you hold the balloon underwater), then V will go down (balloon shrinks).If the volume is constant (say, an aerosol can) and the temperature goes up, then P goes up. (Pop!)