For starters, one atom of Cl weighs the same as two molecules of water. Cl is certainly heavier.
But that alone wont do. Methane is a gas and is considerably less dense than water. Consider CH3Cl. It is heavier (molar mass) than water, has one Cl atom yet is less dense than water. On the contrary, H2O < CH2Cl2 < CHCl3 < CCl4 (increasing order of density)
So, it probably makes sense when you have some 'heavy atoms' in the molecule. And in this case, for our liking, the entire molecule happens to be compact too.