The weak spring has its magic in generating advantageous particle distributions. Particles are pushed away (as if a weak spring is inbetween them) from each other. This results in a more lively motion, in less noise (which the liquid FLIP algorithm may generate over time at the surface) and last but not least in fully conserving liquid volume!

If particles have a mass or particle density property attached they are used in the calculations. But they are not required but optional.
If you are filling these properties yourself you should know what you are doing or at least be cautious about it.