Heat transfer is affected by both, molecular weight and pressure drop. Molecular weight affects the properties of the working fluid and adiabatic index ( Cp/Cv) which directly influence the heat transfer and consequently heat transfer coefficient.
On the other hand pressure drop signifies the operating conditions and mainly velocity. The convective heat transfer is dependent on the velocity of the working fluid and so does heat transfer coefficient.
Heat transfer coefficient defined as a function of Prandtl Number, Pr, a non-dimensional variable of bulk fluid properties depends on Mu, Cp & k. Mol. Wt is not a bulk fluid property. Pressure drop on the other hand, can alter the local velocity, u of open flow systems and hence changes in Reynolds No, Re can change Nusselt Number, Nu, a function of Re & Pr. Any influence of micro molecular properties can enter heat transfer analysis only through bulk fluid properties of open systems.