How can we share parameters within large language models to significantly reduce memory costs while preserving accuracy? While parameter sharing is a promising solution to the memory overhead of large language models, existing methods rely on naive grouping and fail to correct sharing-induced discrepancies. We propose an accurate and efficient parameter sharing framework, SharVeT (Similarity-aware sharing with Vector-based Tuning), which performs similarity-based grouping to ensure accurate sharing, allocates parameters adaptively to preserve diversity within each group, and applies lightweight refinement with knowledge distillation to correct sharing-induced discrepancies. Experiments show that SharVeT outperforms existing sharing methods, achieving up to 32.1% lower perplexity and 23.3% higher few-shot reasoning accuracy.