Semiconductor moiré superlattices have been shown to host a wide array of interaction-driven ground states. However, twisted homobilayers have been difficult to study in the limit of large moiré wavelength, where interactions are most dominant, and despite numerous predictions of nontrivial topology in these homobilayers, experimental evidence has remained elusive. Here, we conduct local electronic compressibility measurements of twisted bilayer WSe₂ at small twist angles. We demonstrate multiple topological bands which host a series of Chern insulators at zero magnetic field near a ‘magic angle’ around 1.23^o. Using a locally applied electric field, we induce a topological quantum phase transition at one hole per moiré unit cell. Furthermore, by measuring at a variety of local twist angles, we characterize how the interacting ground states of the underlying honeycomb superlattice depend on the size of the moiré unit cell. Our work establishes the topological phase diagram of a generalized Kane-Mele-Hubbard model in tWSe₂, demonstrating a tunable platform for strongly correlated topological phases.