Active learning, a widely adopted technique for enhancing machine learning models in text and image classification tasks with limited annotation resources, has received relatively little attention in the domain of Named Entity Recognition (NER). The challenge of data imbalance in NER has hindered the effectiveness of active learning, as sequence labellers lack sufficient learning signals. To address these challenges, this paper presents a novel re-weighting-based active learning strategy that assigns dynamic smoothing weights to individual tokens. This adaptable strategy is compatible with various token-level acquisition functions and contributes to the development of robust active learners. Experimental results on multiple corpora demonstrate the substantial performance improvement achieved by incorporating our re-weighting strategy into existing acquisition functions, validating its practical efficacy. We will release our implementation upon the publication of this paper.