Figure 1 – Weight ‘A’ equals weight ‘B’
‘C’ is a closed container with air at ambient pressure.
The system is in balanced with zero force exerted by weight ‘A’ on the air volume in container ‘C’.

Figure 2 – The centre of the balance has shifted towards weight ‘A1’.
A force is exerted by weight ‘A1’ equal to the opposite force of the compressed air volume of container ‘C1’.
The system is at equilibrium.

At each point between the trajectory from ‘A’ to ‘A1’ the system is at equilibrium.
The setup is close to ideal with low friction. 
The system should be viewed as continuously oscillating between figure 1 and figure 2 and back to figure 1 with only a minimal force being applied to either ‘A’ or ‘B1’.

Figure 3 – Identical setup to figure 1 with the same volume of air in closed container ‘C’.
Mass ‘D’ has the same density/specific weight as the air volume in container ‘C’. (Or actually slightly higher in order to rest on the bottom of container ‘C’).

Figure 4 – Identical setup as figure 2 with compression of air volume in container ‘C’.
Mass ‘D’ will move upwards to position ‘D1’ as a result of the difference in air density.

The movement of ‘D’ to ‘D1’ does not change the pressure exerted by ‘C1’ on the bottom of ‘A1’?

The movement of ‘D’ to ‘D1’ constitutes ‘work’?