Walled cells of plants, fungi and bacteria, come with a large range of shapes and sizes, which are ultimately dictated by the mechanics of their cell wall. This stiff and thin polymeric layer encases the plasma membrane and protects the cells mechanically by opposing large turgor pressure derived stresses. To date, however, we still lack a quantitative understanding for how local and/or global mechanical properties of the wall support cell morphogenesis. Here, we combine super-resolution imaging, and laser-mediated wall relaxation, to quantitate subcellular values of wall thickness (h) and bulk elastic moduli (Y) in large populations of live mutant cells and conditions affecting cell diameter in the rod-shaped model fission yeast.We find that lateral wall stiffness, defined by the surface modulus, σ=hY, robustly scales with cell diameters. This scaling is valid in tens of mutants covering various functions, within the population of individual isogenic strains, along single misshaped cells, and even across the fission yeasts clade. Dynamic modulations of cell diameter by chemical and/or mechanical means suggest that the cell wall can rapidly adapt its surface mechanics, rendering stretched wall portions stiffer than unstretched ones. Size-dependent wall stiffening constrains diameter definition and limits size variations, and may also provide and efficient mean to keep elastic strains in the wall below failure strains potentially promoting cell survival. This quantitative set of data impacts our current understanding of the mechanics of cell walls, and its contribution to morphogenesis.