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Multi-modal large language models (MLLMs) with impressive perception and understanding capabilities will enable a range of downstream applications. However, their substantial computational and memory requirements hinder the real-world implementation, particularly for resource-constrained edge devices. Quantization has emerged as an effective solution for deploying large models. While post-training quantization (PTQ) successfully retains the performance at moderate bit-width (e.g., W8A8), it suffers from severe performance degradation under low-bit quantization (e.g., W4A8), especially for small-scale models that are more suitable for edge deployment. In this paper, we propose ProQuant, a novel weight-activation quantization-aware training (QAT) framework tailored for low-bit MLLMs. First, to align the limited finetuning dataset distribution with the pretrained dataset distribution, we propose a self-relabeling (SRL) scheme to resample the responses of the open-source multimodal dataset. Second, we are the first to take a decoupled view of multi-modal (MM) understanding and language modeling abilities. We propose a progressive block activation (PBA) mechanism to prioritize the MM understanding recovery. We also introduce a vision-sensitive factor $\vecτ$ that effectively identifies the MM-critical layers. Extensive experiments across various benchmarks, covering models with 2B-8B parameters, show that ProQuant significantly outperforms existing methods. For example, our W4A8 Qwen3-VL-2B-Instruct improves average accuracy by impressively 6.6% and achieves performance comparable to full precision counterparts with only approximately 1% performance drop. Code is available at https://github.com/yufeixue-ai/ProQuant/.