The primary reason is that density of an atom increases as you go down the periodic table, and oxygen and hydrogen are very high in that table (are low-density atoms), so all pretty well any cation (for H) or anion (for O) will increase density just by being added even if nothing else happens except replacing those atoms in space. The mass of an atom increases a lot faster than its unit volume.
That is, mass of an atom (ion) doubles way before its volume doubles, so density (mass/volume) goes up. Sulfur (mass 32) does not occupy twice the volume of O (mass 16), as an example, so adding sulfide ion leads to an increase in density (a little more complicated with SO4 or sulfate ion but same general idea).
That is not all that happens, of course, but that is the primary reason. Ions also cause the structure of water to change, which can also affect density (sometimes increasing it, sometimes lowering it a bit but not enough to offset the increased density of the higher atomic number atoms).