The stability of nonvolatile thin liquid films and of sessile droplets is strongly affected by finite size effects. We analyze their stability within the framework of density functional theory using the sharp kink approximation, i.e., on the basis of an effective interface Hamiltonian. We show that finite size effects suppress spinodal dewetting of films because it is driven by a long-wavelength instability. Therefore nonvolatile films are stable if the substrate area is too small. Similarly, nonvolatile droplets connected to a wetting film become unstable if the substrate area is too large. This instability of a nonvolatile sessile droplet turns out to be equivalent to the instability of a volatile drop which can attain chemical equilibrium with its vapor.