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 LVLM 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.