Is molecular mass and molecular size related?

Sometimes

Not exactly, although they can be.  If two molecules are both composed of the same elements, the one that has more atoms in it, the one with more atoms will have a larger molecular mass, and a larger molecular size.  However, different elements weigh different amounts. 

Take for example the molecule octane, which is an ingredient in gasoline, with formula C₈H₁₈. Octane is relatively large, and has a molecular mass of approximately 114 grams per moles.  However, a single atom of the element lead, Pb, is much smaller than the molecule octane, and yet the molar mass of lead is 207.2 grams per mole!  So it is much heavier, and yet smaller.

On the other hand, hydrogen gas (H₂) has a molar mass of 2 grams per mole, and chlorine gas (Cl₂) has a molar mass of 71 grams per mole, and Cl₂ is indeed much larger than H₂.

And so you can see that it depends on the composition of the things you are comparing.