What is the difference between low-density and high-density Polymethyl methacrylate (PMMA) on a molecular level?
Low density and high density PMMA differ by density, which is given as the ratio of mass and volume.

Given that they are prepared from the same monomer, two polymers with the same number of monomers will have the same mass.

If the polymers differ in density, this must be due to the fact that they occupy different volumes.

Note that we are talking about polymers here and not the ordered packing of molecules in a crystal. Nevertheless, inter- and intramolecular interactions (and thus "packing") is important here as well.

As a rule of thumb, polymers with higher branching will "pack" less tightly and thus occupy a higher volume. 

This results in a lower density.