Why does the thickness of the heart's chamber walls vary?

A chamber wall's thickness is directly linked to its function. Each of the 4 chambers has a different function and so, they each have different wall thickness.

The more work a chamber has to do, the thicker the wall.

This explains why the left ventricle of the heart has a thicker wall than the right ventricle - this is because the left ventricle pumps blood all around the body at high pressure whereas the right ventricle only needs to pump the blood to the lungs, which are nearby.