Suppose you are in a boat floating in a swimming pool. There is a stone lying on the bottom of the boat. You pick it up, and throw it overboard. Will the water level rise, fall, or remain unchanged?

It will remain unchanged the weight of the stone in the boat will cause the same amount of water displacement as it would in the water.

When the stone is in the boat it displaces its own weight of water. When it is thrown into the pool it displaces its own volume of water. As the stone is more dense than water it displaces more water due to its weight than due to its volume.
The water level falls.
(This assumes the stone is more dense than the water and sinks. If it is, say, pumice stone and it floats, then the water level will stay the same.)
However, I would think that even with a small pool and a large stone you would be hard put to notice the difference in water level!