We present direct and linear measurements of the normal stiffness and damping of a confined, few molecule thick water layer. The measurements were obtained by use of a small amplitude (0.36 Angstrom), off-resonance atomic force microscopy technique. We measured stiffness and damping oscillations revealing up to seven molecular layers separated by 2.526+/-0.482 Angstrom. Relaxation times could also be calculated and were found to indicate a significant slow-down of the dynamics of the system as the confining separation was reduced. We found that the dynamics of the system is determined not only by the interfacial pressure, but more significantly by solvation effects which depend on the exact separation of tip and surface. The dynamic forces reflect the layering of the water molecules close to the mica surface and are enhanced when the tip-surface spacing is equivalent to an integer multiple of the size of the water molecules. We were able to model these results by starting from the simple assumption that the relaxation time depends linearly on the film stiffness.