Say that I have a vertical thermally insulated cylinder which contains an ideal monoatomic gas under a weightless piston and the system is initially in equilibrium.
Now if a load of weight $W$ is kept on the piston,the piston would fall by some distance and the system would attain a new equilibrium. It is intuitive that the sum of the work done by gravity and the work done by atmospheric pressure would change into internal energy of the gas.
However, my book mentions that only the work done by gravity goes into the increase in internal energy of gas. It does not say anything about where the atmospheric work would go. Why is it so?