Temperature- and stiffness-dependent edge forces offer new mechanisms of designing nanodevices driven by temperature and stiffness gradients. Here, we investigate the edge forces in a graphene nanolayer on a spring supported graphene substrate based on molecular dynamics (MD) simulations. The dependences of the edge forces on the temperature and stiffness of the substrate are discussed in detail. Special attention is paid to the effect of the out-of-plane deformation of the substrate on the constituent edge forces and the resultant edge force. The results show that the deformation may lead to a significant redistribution of the constituent edge forces but does not change the resultant edge force, suggesting that particular caution should be exercised in designing nanodevices based on sliding graphene layers to avoid potential edge damage.