Singular Value Decomposition (SVD) has become an important technique for reducing the computational burden of Vision Language Models (VLMs), which play a central role in tasks such as image captioning and visual question answering. Although multiple prior works have proposed efficient SVD variants to enable low-rank operations, we find that in practice it remains difficult to achieve substantial latency reduction during model execution. To address this limitation, we introduce a new computational pattern and apply SVD at a finer granularity, enabling real and measurable improvements in execution latency. Furthermore, recognizing that weight elements differ in their relative importance, we adaptively allocate relative importance to each element during SVD process to better preserve accuracy, then extend this framework with quantization applied to both weights and activations, resulting in a highly efficient VLM. Collectively, we introduce~\textit{Weighted SVD} (WSVD), which outperforms other approaches by achieving over $1.8\times$ decoding speedup while preserving accuracy. We open source our code at: \href{https://github.com/SAI-Lab-NYU/WSVD}{\texttt{https://github.com/SAI-Lab-NYU/WSVD}