When I was very young I was always amazed that water didn't come shooting up out of the first ice-fishing hole of the season, due to the weight of all the ice. It doesn't, because the weight of the same volume of liquid water would be even heavier. Ice floats, and the thicker the ice, the lower the level of water sits down inside the hole.
There is no additional hydrostatic pressure in the water beyond that due to gravity, because if there were, the ice would have been slowly pushed up to a new equilibrium position fairly quickly.
If I extended this thinking to volcanism, I'd wonder why volcanos can sometimes have high velocity ejecta, and also build cones from liquid that rise high above the local surface. I am guessing that the height of the cone represents effects due to hydrostatic pressure beyond that due to the weight of material above (rock being less flexible than ice) but the high speed ejecta that falls far from the cone is accelerated by gas coming out of solution.
Is the momentum of a volcano's high-velocity ejecta mostly due to expanding gas?
above: Example of an ice-fishing hole, from here.