We study melting mechanisms in single and polycrystalline colloidal films composed of diameter-tunable microgel spheres with short-ranged repulsive interactions and confined between two glass walls. Thick films (>4 layers), thin-films (≤4 layers), and monolayers exhibit different melting behaviors. Thick films melt from grain boundaries in polycrystalline solid films and from film-wall interfaces in single-crystal films; a liquid-solid coexistence regime is observed in thick films but vanishes at a critical thickness of 4 layers. Thin solid films (2 to 4 layers) melt into the liquid phase in one step from both grain boundaries and from within crystalline domains. Monolayers melt in two steps with a middle hexatic phase.