Re: Why does the weight of a cup of water increase when I dip my finger in it?

You ARE applying a force on the water.  There is an upward buoyant force 
on your finger exerted by the water.  (That is how you would float if you 
jumped in.)  By Newton's third law, there is an equal downward force 
exerted on the water by your finger.  It is this force that registers on 
the scale.  Another way to get the same answer is to realize that when you 
put your finger in the water, the level rises.  You can observe this 
rise.  The pressure on the bottom equals rho g h where h is the depth of 
the water.  Since h increases when you put your finger in, the pressure on 
the bottom increases.  That the two answers are the same is an 
illustration of Archimedes' principle.