Metal atoms adsorbed on few-layer graphenes condense to form nanometer-size droplets whose growth is size limited by a competition between the surface tension and repulsive electrostatic interactions from charge transfer between the metal droplet and the graphene. For situations where the work-function mismatch is large and the droplet surface tension is small, a growing droplet can be unstable to a family of shape instabilities. We observe this phenomenon for Yb deposited and annealed on few-layer graphenes and develop a theoretical model to describe it by studying the renormalization of the line tension of a two-dimensional droplet by repulsive interparticle interactions. Our model describes the onset of shape instabilities for nanoparticles where the growth is size limited by a generic repulsive potential and provides a good account of the experimentally observed structures for Yb on graphene.