The success of Large Vision Models (LVMs) is accompanied by vast data volumes, which are prohibitively expensive in medical diagnosis.To address this, recent efforts exploit Parameter-Efficient Fine-Tuning (PEFT), which trains a small number of weights while freezing the rest.However, they typically assign trainable weights to the same positions in LVMs in a heuristic manner, regardless of task differences, making them suboptimal for professional applications like medical diagnosis.To address this, we statistically reveal the nature of sparsity and hybridity during diagnostic-targeted fine-tuning, i.e., a small portion of key weights significantly impacts performance, and these key weights are hybrid, including both task-specific and task-agnostic parts.Based on this, we propose a novel Sparsity- and Hybridity-inspired Parameter Efficient Fine-Tuning (SH-PEFT).It selects and trains a small portion of weights based on their importance, which is innovatively estimated by hybridizing both task-specific and task-agnostic strategies.Validated on six medical datasets of different modalities, we demonstrate that SH-PEFT achieves state-of-the-art performance in transferring LVMs to medical diagnosis in terms of accuracy. By tuning around 0.01% number of weights, it outperforms full model fine-tuning.Moreover, SH-PEFT also achieves comparable performance to other models deliberately optimized for specific medical tasks.Extensive experiments demonstrate the effectiveness of each design and reveal that large model transfer holds great potential in medical diagnosis.