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We introduce ZOOMER, a system deployed at Taobao, the largest e-commerce platform in China, for training and serving GNN-based recommendations over web-scale graphs. ZOOMER is designed for tackling two challenges presented by the massive user data at Taobao: low training/serving efficiency due to the huge scale of the graphs, and low recommendation quality due to the information overload which distracts the recommendation model from specific user intentions. ZOOMER achieves this by introducing a key concept, Region of Interests (ROI) in GNNs for recommendations, i.e., a neighborhood region in the graph with significant relevance to a strong user intention. ZOOMER narrows the focus from the whole graph and "zooms in" on the more relevant ROIs, thereby reducing the training/serving cost and mitigating the information overload at the same time. With carefully designed mechanisms, ZOOMER identifies the interest expressed by each recommendation request, constructs an ROI subgraph by sampling with respect to the interest, and guides the GNN to reweigh different parts of the ROI towards the interest by a multi-level attention module. Deployed as a large-scale distributed system, ZOOMER supports graphs with billions of nodes for training and thousands of requests per second for serving. ZOOMER achieves up to 14x speedup when downsizing sampling scales with comparable (even better) AUC performance than baseline methods. Besides, both the offline evaluation and online A/B test demonstrate the effectiveness of ZOOMER.