You carefully drop a stone into a beaker full of water. The stone sinks to the bottom and water spills out. What can you say about the weight of the displaced water

The weight of the displaced water is equal to the upthrust acting on the stone which is less than the weight of the stone thus the stone sinks to the bottom of the beaker. This is according to the Archimedes principle which states that when an object is partially or wholly immersed in a fluid the weight of the displaced fluid is equal to the upthrust acting on the object.