Music understanding and reasoning are central challenges in the Music Information Research field, with applications ranging from retrieval and recommendation to music agents and virtual assistants. Recent Large Audio-Language Models (LALMs) have shown remarkable progress in answering music-related questions by following user instructions. However, their massive scale, often billions of parameters, results in expensive training, slow inference, and limited deployability on edge devices. In this work, we present TinyMU, a lightweight (229M) Music-Language Model (MLM) that achieves performance comparable to much larger LALMs while remaining efficient and compact. To train TinyMU, we introduce MusicSkills-3.5M, a carefully curated, music-grounded question-answering dataset with 3.5M samples. Spanning multiple-choice, binary, and open-ended formats, this dataset provides fine-grained supervision across diverse musical concepts. For its architecture, TinyMU leverages MATPAC++, the SOTA self-supervised audio encoder for fine-grained feature extraction. Paired with a lightweight linear projector, it efficiently aligns audio embeddings with the language model. Through extensive evaluation, we show that TinyMU performs strongly in both basic music understanding and complex reasoning. Notably, on the MuChoMusic benchmark, it achieves 82\% of SOTA LALM's performance despite being 35x smaller, highlighting the potential of small MLMs under constrained computational budgets.