We describe a series of surface-leveling experiments in glassy polystyrene of varying molecular weight. The evolution through a mobile surface layer is described by the glassy thin film equation that was introduced and used in a previous work. Excellent agreement with the data is achieved, with surface mobility as the single free parameter. Different molecular-weight dependencies in mobility are then observed above and below the glass transition. The results are discussed in terms of surface-chain anchoring in the bulk matrix and the length scale for surface mobility.