Denpressure: 0
Gravity: 2
The ideal gas laws are all that's required to understand and quantify these experiments, they are extremely well known and date back to the 1830's, and for anyone interested the ideal gas laws can be derived completely from first principles ( only minimal assumptions ) using the kinetic theory of gases.
Back to the balloon experiment, I have an easier and more direct method that anyone can easily apply.
Get a long straight stick and find the balance point using a knife edge, mark that point, now get another stick a little less than half the length of the first. Use it to mark off equal distances from the center balance point. Mark those points and now tie short equal length pieces of fishing line to those two points. Get two balloons and with both un-inflated tie the balloons to the fishing lines, check that it still balances perfectly, if not adjust the center support point till it balances exactly.
Now inflate just one of the balloons, with a bicycle pump or similar, place back on the knife edge and see if the inflated balloon is heavier or not. This method eliminates the need for precision scales. You could now add small weights to the lighter side to see how much is required to balance it, maybe grains of rice?
Instead of a knife edge you could hang the thing from the roof with fishing line.