The effects of the molecular weight on the physical aging of polymers were investigated by means of differential scanning calorimetry (DSC) experiments in five PMMA samples with mass values across the entanglement mass M,. The Tool-Narayanaswamy-Moynihan (TNM) model and a recent configurational entropy approach were systematically compared with the experiments. For the samples with the lowest molecular weights, the two approaches exhibited similar agreement with experiments; however, in the systems with higher molecular weights, the TNM model met major difficulties, and a clear improvement was obtained with the other model. The additional parameter introduced by the entropic model showed a strong molecular-weight dependence, with a sharp increase at the entanglements mass of PMMA. These results evidence the role of the chain entanglements on the physical aging of polymers. Finally, the influence of the molecular weight on the fragility was investigated and related to the recent literature debates on this topic.