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MnBi₂Te₄ is an emergent material platform for exploring topological phenomena owing to its intrinsic magnetic order combined with nontrivial topology. Bulk crystal has an A-type antiferromagnetic (AFM) order below its Neel temperature, while the layer dependent magnetism of thin flakes remains largely unexplored. It is unclear how the bulk band structure changes when the magnetic states are tuned by an external field, which is crucial for understanding the topological phase transition in this system. In this work, we probe the intrinsic magnetism of atomically thin MnBi₂Te₄ samples by reflective magnetic circular dichroism (RMCD), and correlate their magnetic order with transport measurements. We show that in thin flake the remnant magnetization and critical spin-flop field exhibit even-odd layer number effects. For both even and odd layers, applying a magnetic field drives the layered AFM state into a canted AFM state, and finally a ferromagnetic (FM) state. The tuning of magnetic states corresponds to concurrent topological phase transitions with a Chern number from C=0 to C=-1.