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Large Vision-Language Models (LVLMs) with only 7B parameters have shown promise as automated judges in chart comprehension tasks. However, tiny models (<=2B parameters) still perform poorly as judges, limiting their real-world use in resource-constrained settings. To address this, we propose two approaches to ensure cost‐efficient evaluation: (i) multi-criteria prompting, which combines separate evaluation criteria into a single query, and (ii) domain‐adaptive transfer learning, in which we fine‐tune a 2B‐parameter VLM on synthetic judgments in a chart dataset to create the ChartJudge. Experiments show that multi-criteria prompting exposes robustness gaps, which led to a huge drop in performance for 7B models, including specialized LVLM judges like LLaVA‐Critic. In addition, we find that our tiny LVLM (ChartJudge) can effectively transfer knowledge from one dataset to another to make it a more specialized model. Our fine-grained analysis across chart types and query complexities offers actionable insights into trade-offs between model size, prompt design, and transferability, enabling scalable, low-cost evaluation for chart reasoning tasks. Our code and the data will be made publicly available.