Vector databases rely on Hierarchical Navigable Small World (HNSW) indexes for similarity search, but a graph built from data alone can be poorly matched to a skewed or changing query workload. We present REWEAVE (Reward-Guided Rewiring of Vector Graphs), an online index-maintenance method that learns edge utility from query feedback and periodically rewires the bottom layer within the original per-node degree cap. The method supports sparse exact-neighbor feedback combined with self-labels, and standard HNSW serving without learning overhead once adaptation is disabled. Under explicit assumptions we prove value-estimation and graph-stabilization guarantees. Under stationary skew, REWEAVE improves held-out recall by up to 23.3 percentage points over HNSW. In comparisons with query-aware baselines on up to 100M vectors, it achieves up to 3.3x NGFix's query throughput at recall@100 of 0.80. On Amazon-ESCI with query drift, it increases stream recall@100 from 0.745 to 0.979 with 34% fewer search distance computations than frozen HNSW. These results illustrate the potential to improve retrieval quality and reduce search effort within an existing graph-degree budget, while incurring additional work during adaptation.

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