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Surface stress and energy are basic quantities in the Gibbsian formulation of the thermodynamic description of surfaces which is central in the formation and long-term behavior of materials at the nanoscale. However, their size dependence is a puzzling issue. It is even unclear whether they decrease or increase with decreasing particle size. In addition, for a given metal, estimates often span over an order of magnitude, far apart from bulk data, which, in the absence of any explicit size-dependence rule, escapes understanding. Here, we combine X-ray absorption and nanoplasmonics data with atomistic simulation to describe α-Al2O3(0001)-supported silver particles. By comparison to MgO(001)-supported and embedded silver, we distinguish epitaxial and surface stress. The latter is shown to dominate above 3 nm in size. Since the observation mostly relies on surface/bulk ratio, a metal-independent picture emerges that is expected to have far-reaching consequences for the understanding of the energetics of nanoparticles.