The examination of the roughness evolution of open-surface resist films during development may elucidate the material origins of Line Edge Roughness. In this paper, a stochastic simulator of resist development is used and the surface roughness evolution is analyzed with dynamic scaling theory. A power-law increase of rms roughness and correlation length is found for resists with homogeneous solubility. The scaling exponents are shown to obey the dynamical scaling hypothesis of Family-Viscek. The insertion of inhomogeneity in the solubility of resist causes much larger increase of rms roughness and anomalous scaling behaviour. Comparison with experimental results shows good agreement with the simulation predictions.