Why doesn't a closed paper bag collapse under the weight of earth's atmosphere?

Answer 1

The bag does not collapse because the air pressure acting on the inside of the bag is equal to the air pressure outside the bag (There are the same number of air molecules per unit volume inside the bag as outside).

However if you had filled the bag with air at high altitude where the air pressure is lower, then sealed it and brought the bag down to sea level you would find that the higher external air pressure (there are fewer air molecules per unit volume inside the bag than outside) would begin to compress the bag down to a smaller volume.

This in turn would compress the air inside the bag leading to an increase in its pressure. This decrease in volume will continue until the air inside the bag is compressed to the point where its pressure is equal to that of the external air pressure.

For further information on this topic it may be worth searching for the term "Combined Gas Law" which will explain the relation between pressure, temperature and volume.