Drain the water and see what happens.

Why are they waterlogged? Don't they drain?

If the peat pot is sitting in standing water (is that what you mean by "over water"?), it will suck up the water effectively and become waterlogged. Lots of good reasons not to use peat pots, but this is one. Get rid of the standing water, and let the pots dry out naturally. The soil inside them will stay moist long after the exterior of the pot is dry.

You can bottom-water with peat pots, but don't leave them standing in water permanently. Just put enough water in the bottom of the pan for them to soak it up in a few hours.