Why does an object when filled with water sink, but without water inside float (in a body of water)? Why does an object sink when filled with water, even if the same object would float without water inside?
For example, put an empty glass cup into water, and it floats.
But if you put a plastic container filled with water in water, it'll sink. Why is that?
 A: For a given volume, light things float and heavy things sink.  The cup sinks when you fill it with water because it becomes heavier, and therefore more dense.  When the cup becomes more dense than water, it sinks.
The cup would sink just as well if you filled it with rocks, lead, etc.  The condition for the cup to sink is that its weight must be greater than the weight of the water it displaces (i.e. its weight must be greater than the weight of a cup exactly the  same size, but made out of water and filled with water.)
You can read a number of other questions on similar material here: https://physics.stackexchange.com/questions/tagged/buoyancy
A: The cup will sink if and only if the total downward force pushing on all its upward facing surfaces, plus its own weight, is stronger than the total upward force pushing on its downward facing surfaces. 
If the cup is full, then the weight of the water inside it pushes down on the upward facing surface of the inside of the bottom of the cup (and possibly one or more internal side surfaces, if they are at an angle), in addition to the weight of all the air above it.
If the cup is empty then only the weight of the air inside the cup is pushing down on it, in addition again to the weight of all the air above it.
Since water is heaver than air, there is more force pushing down on a cup with water in it than a cup without water in it, and so it is more likely to sink. It's really the same reason that a cup of water feels heavier than a cup of air.
