A body of weight w_1 is hung from the ceiling of a room via a chain...

Consider the body and the chain as a single system.

The total downward force acting on this system is the sum of their weights, which is $w_1 + w_2$.

Since the system is in equilibrium, the upward force exerted by the ceiling must balance the total downward force.

Therefore, the ceiling pulls the chain with an upward force equal to $w_1 + w_2$.

Alternatively, considering the free body diagram of the chain, the downward forces acting on it are its own weight $w_2$ and the downward pull from the body $w_1$.

Let the upward force exerted by the ceiling be $T$.

For equilibrium of the chain, $T = w_1 + w_2$.