We quantify sliding stability and rupture styles for a horizontal interface between an elastic layer and stiffer elastic half-space with a free surface on top and rate-and-state friction on the interface. This geometry includes shallowly dipping subduction zones, landslides, and ice streams. Specific motivation comes from quasi-periodic slow slip events on the Whillans Ice Plain in West Antarctica. We quantify the influence of layer thickness on sliding stability, specifically whether steady loading of the system produces steady sliding or sequences of stick-slip events. We do this using both linear stability analysis and nonlinear earthquake sequence simulations. We restrict our attention to the 2D antiplane shear problem, but anticipate that our findings generalize to the more complex 2D in-plane and 3D problems. Steady sliding with velocity-weakening rate-and-state friction is linearly unstable to Fourier mode perturbations having wavelengths greater than a critical wavelength (λ_c). We quantify the dependence of λ_c on the rate-and-state friction parameters, elastic properties, loading, and the layer thickness (Η). We find that λ_c is proportional to sqrt(Η) for small Η and independent of Η for large Η. The linear stability analysis provides insight into nonlinear earthquake sequence dynamics of a nominally velocity-strengthening interface containing a velocity-weakening region of width W. Sequence simulations reveal a transition from steady sliding at small W to stick-slip events when W exceeds a critical width (W_cr), with W_cr proportional to sqrt(H) for small H. Overall this study demonstrates that the reduced stiffness of thin layers promotes instability, with implications for sliding dynamics in thin layer geometries.