We investigate the influence of strain-sharing and finite-size effects on the morphological instability of hetero-epitaxial nanomembranes made of a thin film on a thin freestanding substrate. We show that long-range elastic interactions enforce a strong dependence of the surface dynamics on geometry. The instability time-scale tau is found to diverge as (e/H)(-alpha) with alpha = 4 (respectively 8) in thin (resp. thick) membranes, where e (resp. H) is the substrate (resp. nanomembrane) thickness, revealing a huge inhibition of the dynamics as strain sharing decreases the level of strain on the surface. Conversely, tau vanishes as H-2 in thin nano-membranes, revealing a counter-intuitive strong acceleration of the instability in thin nanomembranes. Similarly, the instability length-scale displays a power-law dependence as (e/H)(-beta), with beta = alpha/4 in both the thin and thick membrane limits. These results pave the way not only for experimental investigation, but also, for the dynamical control of the inescapable morphological evolution in epitaxial systems.