We study metastable behaviour in systems of weakly interacting Brownian particles with localised, attractive potentials which are smooth and globally bounded. In this particular setting, numerical evidence suggests that the particles converge on a short time scale to a " droplet state" which is metastable, i.e. persists on a much longer time scale than the time scale of convergence, before eventually diffusing to 0. In this article, we provide rigorous evidence and a quantitative characterisation...