We have studied surface-stress anisotropy as a function of the thickness of molecular-beam-epitaxy-grown Ge overlayers on the Si(001) substrate. The surface-stress anisotropy changes sign at a dimer-vacancy-line (DVL) periodicity of $\ensuremath{\sim}15.$ By varying the separation between two neighboring DVL's we have also investigated the DVL-DVL interaction. Based on a linear-dipole-force model for the step-step interaction and the theory of long-range elastic relaxation of orientationally inequivalent domains, we have estimated the DVL formation energy of $\ensuremath{-}0.003\mathrm{eV}/\AA{}.$