The electronic structure of weak charge-ordering (CO) state just below the critical pressure in an organic conductor α-(BEDT-TTF)2I3 was experimentally investigated using peak structure in the temperature dependence of interlayer magnetoresistance (MR). Based on a minimal model considering multiple Landau levels (LLs), we discuss herein the MR peak as characteristic to multilayer massless/massive Dirac fermion (DF) systems. MR measured in the weak CO state exhibited a clear MR peak, and its magnetic-field dependence was consistent with the LL behavior of a massive DF with a small gap. Results indicate that the weak CO state in α-(BEDT-TTF)2I3 is a massive DF state.