Next Point-of-Interest (POI) recommendation is a critical task in location-based services, aiming to predict users' next visits based on their check-in histories. While many existing methods leverage Graph Neural Networks (GNNs) to incorporate collaborative information and improve recommendation accuracy, most of them model each type of context using separate graphs, treating different factors in isolation. This limits their ability to model the co-influence of multiple contextual factors on user transitions during message propagation, resulting in suboptimal attention weights and recommendation performance. Furthermore, they often prioritize sequential components as the primary predictor, potentially undermining the semantic and structural information encoded in the POI embeddings learned by GNNs. To address these limitations, we propose a Context-Adaptive Graph Neural Networks (CAGNN) for next POI recommendation, which dynamically adjusts attention weights using edge-specific contextual factors and enables mutual enhancement between graph-based and sequential components. Specifically, CAGNN introduces (1) a context-adaptive attention mechanism that jointly incorporates different types of contextual factors into the attention computation during graph propagation, enabling the model to dynamically capture collaborative and context-dependent transition patterns; (2) a graph-sequential mutual enhancement module, which aligns the outputs of the graph- and sequential-based modules via the KL divergence, enabling mutual enhancement of both components. Experimental results on three real-world datasets demonstrate that CAGNN consistently outperforms state-of-the-art methods. Meanwhile, theoretical guarantees are provided that our context-adaptive attention mechanism improves the expressiveness of POI representations.