Wrinkles in thin films on soft substrates have been shown to self-organize into topological patterns, providing a possible route towards inexpensive generation of surface microstructure. However, the effect of the magnitude of applied stress in relation to the critical buckling stress, or overstress, on the observed patterns has until this point been neglected experimentally. In this paper, we investigate the effect of overstress using poly(dimethylsiloxane) which has been surface-oxidized with a UV-ozone oxidation technique. Using a swelling-based stress application technique, where the applied swelling stress in the thin film is controlled by changing the concentration of vapor-phase swelling agent (ethanol) in a sealed swelling chamber, we are able to impart swelling stresses below, at, and well above the critical stress. We observe a transition from hexagonally packed dimples at low overstress to ridge-based morphologies (herringbone and labyrinth) at high overstress. The observed dimple structures are remarkably widespread, and the hexagonal arrangement of these dimples is confirmed using Fourier analysis. Although analytical results predict that a square arrangement of dimples is preferred to hexagonal for flat wrinkling surfaces, hexagonal arrays are nonetheless unilaterally observed at low overstress. We attribute this observation to an inherent curvature that develops in the swelling film. The overstress is quantified by measuring the radius of curvature of swelling bilayer beams, both confirming the preferential swelling of the surface oxide layer by ethanol and quantifying the swelling extent. Effects of non-equibiaxial stress are investigated by inducing a compressive prestress prior to swelling, and “trapped” non-equilibrium morphologies are discussed briefly.