Small language models (SLMs) are gaining attention for their lower computational and memory needs while maintaining strong performance. However, efficiently deploying SLMs on resource-constrained devices remains a significant challenge. Post-training quantization(PTQ) is a widely used compression technique that reduces memory usage and inference computation, yet existing methods face challenges in inefficient bit-width allocation and insufficient fine-grained quantization adjustments, leading to suboptimal performance, particularly at lower bit-widths. To address these challenges, we propose multi-level weight quantization (MLWQ), which facilitates the efficient deployment of SLMs. Our method enables more effective bit-width allocation by jointly considering inter-layer loss and intra-layer salience. Furthermore, we propose a fine-grained partitioning of intra-layer salience to support the tweaking of quantization parameters within each group. Experimental results indicate that MLWQ achieves competitive performance compared to state-of-the-art methods, providing an effective approach for the efficient deployment of SLMs while maintaining model accuracy.