Multi-level sentence simplification generates simplified sentences with varying language proficiency levels. We propose Label Confidence Weighted Learning (LCWL), a novel approach that incorporates a label confidence weighting scheme in the training loss of the encoder-decoder model, setting it apart from existing confidence-weighting methods primarily designed for classification. Experimentation on English grade-level simplification dataset shows that LCWL outperforms state-of-the-art unsupervised baselines. Fine-tuning the LCWL model on in-domain data and combining with Symmetric Cross Entropy (SCE) consistently delivers better simplifications compared to strong supervised methods. Our results highlight the effectiveness of label confidence weighting techniques for text simplification tasks with encoder-decoder architectures.