The idea is that by including both the Ekman current (induced by the mean wind stress at the surface) and the wave-induced current (Stokes drift), the resulting total surface velocity can be easily represented as a function of wind velocity at 10 meters. Both Ekman and wave-induced currents are about the same size and add up to be around 3% of the wind speed. The assumptions include the full range for Ekman dynamics (homogeneous, not affected by boundaries), plus some about waves (non-decaying, small amplitude). In the real ocean, eddy viscosity is vertically variable, but, as it is the case with Ekman dynamics, the approximation is quite close to what is observed in the ocean. The approximations that Weber used are valid for a large range of wind values (5-30 m s−1) and they break down in weak wind (not fully developed waves) and strong wind conditions (whitecapping, wave breaking).
Weber, J. E., 1983: Steady Wind- and Wave-Induced Currents in the Open Ocean. J. Phys. Oceanogr., 13, 524–530.