A scaling relation between fractal dimension and stability ratio is demonstrated for a charged polystyrene colloid undergoing aggregation. The stability ratio, i.e., the inverse collision efficiency, or inverse sticking probability, is systematically decreased by reducing the electrostatic barrier to aggregation. Fractal dimensions are measured by static light scattering, while stability ratios are evaluated from early-time aggregation kinetics (t < 10t(1/2)) using dynamic light scattering. The fractal dimension for the model hydrophobic colloid investigated increases monotonically with stability ratio, reflecting a continuous increase in particle packing density as the sticking probability is reduced.