Question

How is the size of a planet related to the thickness of its atmosphere

Answer 1

Many planets are made of gas, and in different situations, the atmosphere can be destroyed.

The sun which is burnt measures atmosphere and in the same case planets can be in a good situation on galactic map and a great condition in the atmosphere as well as earth.
For example, the mass of an object can attract a smaller object causing gravity. The bigger the masses of a planet when it is in the right condition the more atmosphere it can attract if there is any floating on the planet. If it is big it will make a gravitational influence and gather more gases.

Answer 2

The bigger the planet the bigger the gravitational pull of the planet , which is also stipulated in Newton Law of gravity. The bigger the planet, therefore, the bigger the atmosphere it would have. This is because its gravity is able to overcome the kinetic energy of the gas molecules (especially when heated by rays from a star they are orbiting) that would allow the gas atoms/molecules to escape into space. This is also why the large planets are all gas giants such as Jupiter.