Multimodal Large Language Models (MLLMs) have shown promise in visual-textual reasoning, with Multimodal Chain-of-Thought (MCoT) prompting significantly enhancing interpretability. However, existing MCoT methods rely on rationale-rich datasets and largely focus on inter-object reasoning, overlooking the intra-object understanding crucial for image classification. To address this gap, we propose WISE, a Weak-supervision-guided Step-by-step Explanation method that augments any image classification dataset with MCoTs by reformulating the concept-based representations from Concept Bottleneck Models (CBMs) into concise, interpretable reasoning chains under weak supervision. Experiments across ten datasets show that our generated MCoTs not only improve interpretability by 37% but also lead to gains in classification accuracy when used to fine-tune MLLMs. Our work bridges concept-based interpretability and generative MCoT reasoning, providing a generalizable framework for enhancing MLLMs in fine-grained visual understanding.