The correlation between molecular mass and boiling point is commonly cited although I believe it's a [grave misconception](http://pubs.acs.org/doi/pdf/10.1021/ed039p454
) and lazy teaching. The correlation does exist but it's to do with the increased strength of the intermolecular interactions and not necessarily due to the increase mass of the molecules. Essentially, heavier atoms and molecules will have more electrons and greater polarizability leading to stronger intermolecular interactions.
Whether or not a large group of molecules will be gas or liquid at a given temperature, pressure etc. is reliant on the energetics of the system. Generally speaking the energy a molecule has is independent of it's mass. Compare the definitions of [root mean squared molecular speed](https://en.wikipedia.org/wiki/Root-mean-square_speed
) and [kinetic energy](https://en.wikipedia.org/wiki/Kinetic_energy#Newtonian_kinetic_energy
). Any change in mass cancels out to give the same amount of energy.
You are right in that the amount of space a molecule takes up also plays a part. Again, this plays back to effect the intermolecular interactions but it also plays it's own role in boiling point determination. The effects these two main properties have on phase determination are summarised in the various equations of state used to determine phase diagrams. The most famous is [van Der Waals](https://en.wikipedia.org/wiki/Van_der_Waals_equation
) where the constants *a* and *b*, simply added as smudge facts to the ideal gas law, are respectively related to the intermolecular attractions and the finite volume the particles make up. This is the first equation of state to truly start predicting phase changes.