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Searching for a more compact network width recently serves as an effective way of channel pruning for the deployment of convolutional neural networks (CNNs) under hardware constraints. To fulfill the searching, a one-shot supernet is usually leveraged to efficiently evaluate the performance \wrt~different network widths. However, current methods mainly follow a \textit{unilaterally augmented} (UA) principle for the evaluation of each width, which induces the training unfairness of channels in supernet. In this paper, we introduce a new supernet called Bilaterally Coupled Network (BCNet) to address this issue. In BCNet, each channel is fairly trained and responsible for the same amount of network widths, thus each network width can be evaluated more accurately. Besides, we propose to reduce the redundant search space and present the BCNetV2 as the enhanced supernet to ensure rigorous training fairness over channels. Furthermore, we leverage a stochastic complementary strategy for training the BCNet, and propose a prior initial population sampling method to boost the performance of the evolutionary search. We also propose the first open-source width benchmark on macro structures named Channel-Bench-Macro for the better comparison of width search algorithms. Extensive experiments on benchmark CIFAR-10 and ImageNet datasets indicate that our method can achieve state-of-the-art or competing performance over other baseline methods. Moreover, our method turns out to further boost the performance of NAS models by refining their network widths. For example, with the same FLOPs budget, our obtained EfficientNet-B0 achieves 77.53\% Top-1 accuracy on ImageNet dataset, surpassing the performance of original setting by 0.65\%.