Fine-tuning biomedical pre-trained language models (BioPLMs) such as BioBERT has become a common practice dominating leaderboards across various natural language processing tasks. Despite their success and wide adoption, prevailing fine-tuning approaches for named entity recognition (NER) naively train BioPLMs on targeted datasets without considering class distributions. This is problematic especially when dealing with imbalanced biomedical gold-standard datasets for NER in which most biomedical entities are underrepresented. In this paper, we address the class imbalance problem and propose WeLT, a cost-sensitive fine-tuning approach based on new re-scaled class weights for the task of biomedical NER. We evaluate WeLT’s fine-tuning performance on mixed-domain and domain-specific BioPLMs using eight biomedical gold-standard datasets. We compare our approach against vanilla fine-tuning and three other existing re-weighting schemes. Our results show the positive impact of handling the class imbalance problem. WeLT outperforms all the vanilla fine-tuned models. Furthermore, our method demonstrates advantages over other existing weighting schemes in most experiments.