Answer
As long as we pull slowly and steadily, the upper string should break first.
Let $T_l$ be the tension in the lower string. Then the tension in the upper string $T_u$ is equal to $T_l+Mg$, where $M$ is the mass of the heavy ball. Since $T_u \gt T_l$, the upper string should break first.
Work Step by Step
As long as we pull slowly and steadily, the upper string should break first.
Let $T_l$ be the tension in the lower string. Then the tension in the upper string $T_u$ is equal to $T_l+Mg$, where $M$ is the mass of the heavy ball. Since $T_u \gt T_l$, the upper string should break first.
(Note that if we pull suddenly on the lower string, it is possible that the lower string will break first. A sudden increase in tension of the lower string may not have time to increase the tension in the upper string before the lower string breaks.)
