Traditional information retrieval (IR) methods excel at textual and semantic matching butstruggle in reasoning-intensive retrieval tasks that require multi-hop inference or complexsemantic understanding between queries and documents. One promising solution is to explicitly rewrite or augment queries using large language models (LLMs) to elicit reasoning relevant content prior to retrieval. However, the widespread use of large-scale LLMs like GPT-4 or LLaMA3-70B remains impractical due to their high inference cost and limited deployability in real-world systems. In this work, we introduce TongSearch QR, a family of small-scale language models for query reasoning and rewriting in reasoning-intensive retrieval. Our approach frames query reformulation as a reinforcement learning problem and employs a novel semi-rule-based reward function. This enables smaller language models (e.g., 7B and 1.5B) to achieve reasoning performance rivaling large-scale LLMs without their prohibitive inference costs. Experiment results on BRIGHT (Su et al., 2024) benchmark show that, with BM25 as retrievers, both TongSearch QR-7B and TongSearch QR-1.5B models significantly outperform existing baselines, including prompt-based query reasoners and some latest dense retrievers trained for reasoning-intensive retrieval tasks, offering superior adaptability for real-world deployment.