If you float a small block of wood in a full glass of water and then measure how much water spills out of the glass, the weight of the spilled water will equal the weight of the floating wood! Discovering this, Greek philosopher Archimedes realized that anything that displaces its own weight in water will float.
But wait you say! I can drop even a small rock into the glass and it sinks right away. How come?
Let's return to our experiment. We have a glass filled to the rim with water. It's sitting in a pie plate, and the pie plate is on a scale. Drop the rock into the glass. Some water will spill over the sides. Now remove the glass and see how much the spilled water weighs. You will find that it weighs less than the rock weighs by itself.
The rock is unable to displace its own weight in water, and so down it goes, just as Archimedes said it would.
Why is the rock unable to displace its own weight when the wood was able to?
Its because the rock has a greater density. Density just means how much stuff there is packed into the object. If we could magically inflate the rock, so it got bigger in size without adding any more stuff to it, its density would go down. Eventually it would be less dense than water and could float.
The rock sinks not because it weighs more than the wood, but because it is too dense to displace its own weight.