Do not blame your son or his weight...
When someone sits on a chair the load is taken by the seat and the legs. These should not break even with two or three big people sitting on one anothers laps.
Leaning back on the chair; so that all the load is taken by the back two legs, places great strain on all the other joints. Strain that will cause the joints to loosen where there's a pulling force and thin spindles (less often) to break where there's a compression force.
Dismantle any loose joints - apply white PVA glue and reassemble. Wind stout rope twice around the outside of the legs with bits of cardboard protecting them from rope damage and then use a small length of wood to twist the rope and apply pressure to close the joints - like a tourniquet. Leave overnight for glue to harden.
Stop the leaning back.
Peccavi
October 2008