Understanding the driving forces of viral capsid assembly can shed light on the treatment of viral diseases. We report a study of the self-assembly of virus-like-particles formed by Cowpea Chlorotic Mottle Virus capsid protein and polystyrene sulfonate (PSS) of five different molecular weights. The goal is to explore the effects of the preferred curvature of the capsid proteins and the molecular weight of the packaged cargo on capsid size. Polymorphism of the capsids size was found with the majority of the capsid diameters converging onto two discrete values that correspond to particular icosahedral symmetries. Further, for each size of PSS packaged, one unique capsid size was found dominant. A model is provided for the formation of the virus-like-particles that account for both the PSS and capsid protein self-interactions, and the interactions between the protein and PSS. This study suggests that the size of the encapsidated polymer cargo is the deciding factor for the selection of one distinct capsid size from many possible capsid sizes bearing the same inherent symmetry.