The pressure of the water at the level of the lower end of the tube is the same both inside and outside the tube. Consequently the string is being pulled downwards by the weight of the tube itself less the force of upthrust (the weight of the same volume of water as the tube's capacity), and also the pressure which the water exerts on the closed end of the tube (atmospheric pressure enters into this). And the pressure of the column of water is proportional to the depth of immersion of the closed end of the tube.
In fact, if the open end of the tube be imagined to be closed, nothing will be altered. But then the following forces will act on the strings: the weight of the tube and its contents, the pressure of the column of water above the tube plus atmospheric pressure, and lastly the pressure exerted by the water underneath, which is equal to the weight of a column of water whose height equals the depth of the open end of the tube beneath the free surface of the water, plus atmospheric pressure. But this last force is balanced by the water and the piston inside the tube.