We theoretically study the deformation and elastic response of a supported bilayer membrane subject to the contact of an adhering sphere of radius R. We find that a macroscopic sphere, e.g., R similar or equal to 2 mu m, should adhere over a mesoscopic region similar or equal to 300 Angstrom and relax over a similar length. Due to the coupling between the chevron tilt deformation of the lipids and the membrane thickness gradient, the relaxation develops damped oscillations. A detectable signature of this coupling, which has several important implications, is a change of concavity in the force vs displacement curve.