The fragility of glass describes how rapidly its molecules slow down as it is cooled near its glass transition temperature. In nanoscale films, polymer glasses with higher fragility experience larger reductions in their Tg compared to those with lower fragility. We investigated whether this is due to the free surface of the polymers, which can cause the surface Tg (Tgsurf) to decrease relative to the bulk Tg. By measuring Tgsurf of various polymers, we found that the shift in Tgsurf relative to the bulk Tg increased with fragility. This suggests that more fragile polymers are more susceptible to the free surface effect. We explain this using the concept of energy landscape, as it is used to explain the different slowdown rates between strong and fragile glass formers at Tg.