We use molecular dynamics simulations to study the melting of pentane and hexane monolayers adsorbed on the basal plane of graphite. For both of these systems, the temperature-dependent structures and the melting temperatures agree well with experiment. A detailed analysis reveals that a mechanism involving the promotion of molecules to the second layer underlies melting in these systems. In the second-layer promotion mechanism, a small fraction of molecules transition into the second layer around the melting temperature, leaving vacant space in the first layer to facilitate disordering. The second-layer promotion mechanism arises because of the weaker molecule-surface interaction in our study than that in previous studies. The weaker molecule-surface interaction is consistent with experimental temperature-programmed desorption studies.