If you know the size distribution and the shape distribution curves, you may get the weight distriution curve of the particles. From that you can get the "average degree of polymerization" which, however, in my opinion is not really meaningful.

If I understand correctly, I do not think you require molecular weight of graphene, if you are dealing with the properties of a single graphene sheet. Be it any extensive property like specific heat, conductivity or any other, all this will depend upon total mass of the graphene sheet or total number of carbon atoms composing the sheet. In that scenario, it would be useful to define molar specific heat or moalr conductivity based on that of carbon alone. On the other hand if you have several graphene 'molecules' present in your sample, you should define it based on average mass of the sheet.