A theory for non-Gaussian transport, based on concepts from percolation theory, is applied here to the development of weathering rinds on surface and near surface clasts. In this theory, solute transport through heterogeneous media behaves distinctly from the fluid flow. In particular, although the solute transport velocity and fluid velocities are identical at the scale of a single pore, as transport distances increase, the solute velocity diminishes approximately as a power law. Solute transport distances, x, thus increase as a sublinear power, q, of the transport time, t, with predicted values of q intermediate between 0.5 and 1.0. The known behavior of the solute transport distance as a function of time turns out to be identical to the observed thickness of weathering rinds as a function of time. The value of q depends on conditions of saturation and dimensional constraints to flow. Fractures, for example, constrain flow to two-dimensional surfaces. Both two- and three-dimensional values were found in nature. However, nearly all the weathering rind studies analyzed yielded values of q consistent with unsaturated conditions. One of three exceptions was the case of submarine basalts, which yielded a q value consistent with saturated conditions, as expected. The cases of the Yakima and Truckee River valley weathering rinds, however, where the values of q also indicated saturated conditions, were less easily explained. On the other hand, four Alpine rind studies analyzed, as well as three others derived from the literature, were all consistent with unsaturated conditions and flow constrained to two dimensions. Microfractures could guide flow along two-dimensional surfaces in Alpine environments. Occurrence of frost shattering of surface clasts in Alpine environments has been cited by other authors. Contrasts in rind thicknesses were found to be generally compatible with contrasts in total solute transport distances when fluid flow velocities were assigned based on geometric mean values of the hydraulic conductivity for a given rock type and gravity flow. However, rind development under Alpine conditions may be slower than expected.