A sessile droplet can deform the surface of a soft solid not only with its weight. The surface tension pulls up a ridge at the perimeter of the drop, and the capillary pressure embosses a quasi-spherical dimple underneath the drop. This holds for the case of a bulk solid. However, if the solid forms a film with thickness comparable to the deformation scale the shape and the depth of the dimple are strongly distorted. We investigated dimples on elastomer films with a Young's modulus of 25 kPa and thickness in the range 4-104 mu m embossed by sessile ionic liquid droplets. The films are supported by an undeformable glass slide. Below a certain critical film thickness, the dimple is shallower and the ridge at the drop rim is less elevated than for the bulk elastomer. The deviations are more pronounced for thinner films. Further, troughs form at the two sides of the ridge. Their distance from the rim is equivalent to the layer thickness. The measurements are qualitatively reproduced by an analytical model and quantitatively by numerical simulations. A consistent physical picture of the deformation on the bulk elastomer and of the distortions on the thin films is given.