The overwhelming volume of content being published at any given moment poses a significant challenge for the design of automated fact-checking (AFC) systems on social media, requiring an emphasized consideration of efficiency aspects.As in other fields, systems built upon LLMs have achieved good results on different AFC benchmarks. However, the application of LLMs is accompanied by high resource requirements. The energy consumption of LLMs poses a significant challenge from an ecological perspective, while remaining a bottleneck in latency-sensitive scenarios like AFC within social media. Therefore, we propose a system built upon fine-tuned smaller BERT-based models. When evaluated on the ClimateCheck dataset against decoder-only LLMs, our best fine-tuned model outperforms Phi 4 and approaches Qwen3 14B in reasoning mode — while significantly reducing runtime per claim. Our findings demonstrate that small encoder-only models fine-tuned for specific tasks can still provide a substantive alternative to large decoder-only LLMs, especially in efficiency-concerned settings.