Polymer melts confined between weakly adsorbing surfaces terminated with methyl groups (close-packed self-assembled monolayers of condensed octadecyltriethoxysilane, OTE) were studied in regard to surface forces (static forces to compress the polymer films to a given thickness) and shear theology. The experiments involved a surface forces apparatus modified for dynamic mechanical shear oscillation. The polymers were an atactic poly(phenylmethylsiloxane), PPMS, with chain length from 31 to 153 skeletal bonds. Three principal conclusions emerged. First, the equilibrated surface force between OTE was zero down to the same small thickness (17 +/- 2 Angstrom) regardless of molecular weight. This decisively confirms theoretical predictions for the surface forces of polymer chains in equilibrium with a bulk reservoir. Second, enhanced effective shear moduli (measured in the Linear-response regime) were observed only at this thickness of measurable surface force. This accompaniment of surface force and enhanced shear modulus was also seen in the case of strong adsorption. But in that case, these phenomena scaled with the molecular size of the polymer, approximately its radius of gyration (R(G)); here these phenomena appeared at a single film thickness. Third, the effective elastic shear modulus G’ under confinement was rubberlike in magnitude, indicating enormously slower relaxation than in the bulk fluid. This relaxation was slower, the higher the polymer molecular weight. This third conclusion is qualitatively similar to the case for these same PPMS polymers confined between strongly adsorbing surfaces. It suggests that, even in the case of weak adsorption, geometrical confinement enhances entanglement interactions between polymer chains.