The present study is in sequel to the previous research (Phys. Chem. Chem. Phys. 16(2014) p. 19122), where a solution-based nucleation and growth approach that involved direct epitaxial nucleation of nanofibres of poly(3-hexylthiophene) (P3HT) on carbon nanotubes (CNTs) for potential use as next-generation building blocks for applications including field-effect transistors and photovoltaic devices, was described. Also presented was a theoretical analysis of epitaxial mechanism of nucleation and growth of semiconducting conjugated polymers notably, P3HT on CNTs. In the present study, we elucidate the impact of molecular weight of P3HT on structural morphology and photophysical properties. The change in average molecular weight of P3HT from similar to 14 to similar to 60 kDa resulted in several structural changes, even though the mechanism of nucleation and growth continued to be epitaxial process. In the case of high-molecular weight P3HT, the crystallized fibrils were similar to 200-400 nm in length and similar to 2-3-nm thick. In contrast, for the low molecular weight, the fibrils were significantly longer (> 5 mu m) in length and similar to 800-1000-nm thick, which are envisaged to involve chain folding in relation to shorter fibrils. Furthermore, the graft density of fibrils crystallized on CNTs was remarkably higher for the high-molecular weight P3HT such that the connectivity between successive fibrils is anticipated to be through very small tie-molecules. On the other hand, the graft density of low-molecular weight P3HT crystallized on CNTs was low. Thus, the interconnectivity between successive fibrils is anticipated to involve large tie-molecules. The differences in connectivity between successive fibrils (besides the structural morphology), for low- and high-molecular weight P3HT, would at least, in part, impact the charge carrier mobility.