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Memristive properties of thin film copper oxides with different grain sizes were characterized using tunneling atomic force microscopy (TUNA) and optical reflection measurements. The thin films containing copper ions of different chemical states were prepared by thermal oxidation of metallic copper thin films, deposited via magnetron sputtering onto silicon wafer substrates at an elevated temperature for various lengths of time. The TUNA measurements showed a memristive hysteresis in the I-V curves under an applied bias profile with an initial bias of -3.5V, a ramp up to 3.5V, and subsequent return to -3.5V. Histogram analysis of the barrier height distribution for the forward and backward bias indicated that the barrier height fluctuates in a narrow range of bias voltages that are related to electrochemical potentials for oxidation/reduction of copper ions. Changes in chemical state of copper atoms were identified by optical reflectance measurements in UV-VIS-NIR wavelength regions. The growth of the thin films, including grain size, were characterized by topographic AFM imaging and changes in optical absorption bands due to the quantum size confinement effects.