Multi-behavior recommendation paradigms have emerged to capture diverse user activities, forecasting primary conversions (e.g., purchases) by leveraging secondary signals like browsing history. However, current graph-based methods often overlook cross-behavioral synergistic signals and fine-grained intensity of individual actions. Motivated by the need to overcome these shortcomings, we introduce Synergy Weighted Graph Convolutional Network (SWGCN). SWGCN introduces two novel components: a Target Preference Weigher, which adaptively assigns weights to user-item interactions within each behavior, and a Synergy Alignment Task, which guides its training by leveraging an Auxiliary Preference Valuator. This task prioritizes interactions from synergistic signals that more accurately reflect user preferences. The performance of our model is rigorously evaluated through comprehensive tests on three open-source datasets, specifically Taobao, IJCAI, and Beibei. On the Taobao dataset, SWGCN yields relative gains of 112.49% and 156.36% in terms of Hit Ratio (HR) and Normalized Discounted Cumulative Gain (NDCG), respectively. It also yields consistent gains on IJCAI and Beibei, confirming its robustness and generalizability across various datasets. Our implementation is open-sourced and can be accessed via https://github.com/FangdChen/SWGCN.