Surface wetting phenomena impact chemistry, physics, biology, and engineering. The wetting behaviors of partially-miscible binary liquid systems are especially complex. Here we report evidence of universal behavior in the divergence of wetting layer growth at liquid-vapor interfaces of the cyclohexane + aniline, hexane + o-toluidine, and methanol + carbon disulfide systems. Layer growth on the micron scale was followed using visible light scattering from stirred samples. Layer thicknesses diverged with decreasing temperature when coexistence was approached from the one-phase region, but only for solutions richer in the higher density / higher surface tension component. The onset of divergence was <1 K above the bulk coexistence temperature; nearer the critical composition, the onset temperature was the critical temperature itself. All three systems showed identical divergent wetting properties after variable normalization. In contrast, no divergent wetting layer formation was seen in the benzene + 1,2-propanediol or water + phenol systems. The mathematical sign of the Hamaker constant correlates with the contrasting behaviors. Collectively, these results have implications for theoretical descriptions of adsorption layer growth and crossover behavior, for measurements of complete wetting temperatures, and for practical applications.