While recent advances in Reinforcement Fine-Tuning (RFT) have shown that rule-based reward schemes can enable effective post-training for large language models, their extension to cross-modal, vision-centric domains remains largely underexplored. This limitation is especially pronounced in the medical imaging domain, where effective performance requires both robust visual perception and structured reasoning. In this work, we address this gap by proposing VRFT-Aug, a visual reinforcement fine-tuning framework tailored for the medical domain. VRFT-Aug introduces a series of training strategies designed to augment both perception and reasoning, including prior knowledge injection, perception-driven policy refinement, medically informed reward shaping, and behavioral imitation. Together, these methods aim to stabilize and improve the RFT process. Through extensive experiments across multiple medical datasets, we show that our approaches consistently outperform both standard supervised fine-tuning and RFT baselines. Moreover, we provide empirically grounded insights and practical training heuristics that can be generalized to other medical image tasks. We hope this work contributes actionable guidance and fresh inspiration for the ongoing effort to develop reliable, reasoning-capable models for high-stakes medical applications.