London dispersion forces - is my reasoning right?

I was thinking about this: as the number of electrons in atoms increases, what happens to the London dispersion forces?

My reasoning is this: as the number of electrons increases along a period, the atom in question becomes smaller owing to greater attraction to the nucleus. This also makes the atom less polarizable (i.e. the electron cloud is harder to distort) and so the London dispersion forces weaken along a period. Only if the increase in the number of electrons leads to an additional electron shell, the molecule becomes bigger and more polarizable, so the London dispersion forces increase.

However, this clashes with the claim that, as a rule of thumb, London dispersion forces increase with an increase in molecular weight. As one moves along period, the molecular weight increases (which would lead me to think that the dispersion forces increase), yet the atoms become smaller (which, by my reasoning above, makes me think that the dispersion forces weaken)!

Which line of reasoning is correct? Is the "molecular weight rule of thumb" only used when comparing molecules as opposed to atoms?