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FPGA accelerators for lightweight neural convolutional networks (LWCNNs) have recently attracted significant attention. Most existing LWCNN accelerators focus on single-Computing-Engine (CE) architecture with local optimization. However, these designs typically suffer from high on-chip/off-chip memory overhead and low computational efficiency due to their layer-by-layer dataflow and unified resource mapping mechanisms. To tackle these issues, a novel multi-CE-based accelerator with balanced dataflow is proposed to efficiently accelerate LWCNN through memory-oriented and computing-oriented optimizations. Firstly, a streaming architecture with hybrid CEs is designed to minimize off-chip memory access while maintaining a low cost of on-chip buffer size. Secondly, a balanced dataflow strategy is introduced for streaming architectures to enhance computational efficiency by improving efficient resource mapping and mitigating data congestion. Furthermore, a resource-aware memory and parallelism allocation methodology is proposed, based on a performance model, to achieve better performance and scalability. The proposed accelerator is evaluated on Xilinx ZC706 platform using MobileNetV2 and ShuffleNetV2.Implementation results demonstrate that the proposed accelerator can save up to 68.3% of on-chip memory size with reduced off-chip memory access compared to the reference design. It achieves an impressive performance of up to 2092.4 FPS and a state-of-the-art MAC efficiency of up to 94.58%, while maintaining a high DSP utilization of 95%, thus significantly outperforming current LWCNN accelerators.