Photons in a nonlinear medium can repel or attract each other, resulting in strongly correlated quantum many-body states1,2. Typically, such correlated states of light arise from the extreme nonlinearity granted by quantum emitters that are strongly coupled to a photonic mode2,3. However, unavoidable dissipation (such as photon loss) blurs nonlinear quantum effects when such approaches are used. Here, we generate strongly correlated photon states using only weak coupling and taking advantage of dissipation. An ensemble of non-interacting waveguide-coupled atoms induces correlations between simultaneously arriving photons through collectively enhanced nonlinear interactions. These correlated photons experience less dissipation than the uncorrelated ones. Depending on the number of atoms, we experimentally observe strong photon bunching or antibunching of the transmitted light. This realization of a collectively enhanced nonlinearity may turn out to be transformational for quantum information science and opens new avenues for generating non-classical light, covering frequencies from the microwave to the X-ray regime.