Automatic simplification can help laypeople to comprehend complex scientific text. Language models are frequently applied to this task by translating from complex to simple language. In this paper, we describe our system based on Llama 2, which ranked first in the PLABA shared task addressing the simplification of biomedical text. We find that the large portion of shared tokens between input and output leads to weak training signals and conservatively editing models. To mitigate these issues, we propose sentence-level and token-level loss weights. They give higher weight to modified tokens, indicated by edit distance and edit operations, respectively. We conduct an empirical evaluation on the PLABA dataset and find that both approaches lead to simplifications closer to those created by human annotators (+1.8% / +3.5% SARI), simpler language (-1 / -1.1 FKGL) and more edits (1.6x / 1.8x edit distance) compared to the same model fine-tuned with standard cross entropy. We furthermore show that the hyperparameter $\lambda$ in token-level loss weights can be used to control the edit distance and the simplicity level (FKGL).