Substrate-film interfacial properties play a fundamental role in the adhesion of glassy polymer thin films onto supporting substrates. Utilizing steered molecular dynamics (SMD) simulations, here we uncover that the cohesive noncovalent forces between polymer chains also have a significant effect on the adhesive properties of polymer films in contact with flat substrates. We demonstrate that weaker interchain interactions, all else being the same, can induce higher adhesion energy within the interface. Three different regimes in the adhesion energy profile can be characterized by a nonlinear scaling relationship. In the weak substrate-film interaction regime, the adhesion energy of the film exhibits near independence of cohesive force variations, and the entropic contributions to the surface free energy are consequential. In the intermediate regime, films with weaker cohesive forces exhibit higher adhesion energy due to the ability of polymer chains to pack more effectively in the interfacial region, thereby increasing the adhesive interaction density. In the strong interaction regime, the adhesion energy increases linearly with the adhesive interaction strength because of saturation of local packing in the interfacial region. These findings corroborate recent polymer dewetting observations that have hinted on the importance of local relaxation and packing effects on interfacial properties.