The high stress is there. Old faults and other weaknesses are everywhere. If fluid is injected, either by man of nature, it tends to counteract the pressure that is holding the fault together (called normal stress). So, the fault becomes weaker. If the shear stress along the fault overcomes the effective stress that is holding the fault together (also related to friction on the fault surface...slippery vs rough...), there will be an earthquake.

Most earthquakes related to water reservoirs are due to the pressure of the water in the cracks, not to the mass of the water in the reservoir...although for a large reservoir, the mass could have an effect: either to make it more or less likely that a fault will fail...it get complicated.
Chris