Here we report a device size and structure dependent study on the resisitive switching and synaptic plasticity in HfO2-based memristive devices. We found that the on/off ratio of resistive switching constantly increases as device size decreases, and bilayer Pt/TaOx/HfO2/Pt devices generally exhibit more uniform switching characteristics and lower threshold voltages compared with single-layer Pt/HfO2/Pt devices. Long-term potentiation and depression behaviors have been emulated using such bilayer devices, suggesting potential applications for neuromorphic hardware.