In precision agriculture, non-invasive remote sensing using UAVs can be employed to observe crops in visible and nonvisible spectra. This paper investigates the effectiveness of stateof-the-art knowledge distillation techniques for mapping weeds with drones, an essential component of precision agriculture that employs remote sensing to monitor crops and weeds. The study introduces a lightweight Vision Transformer-based model that achieves optimal weed mapping capabilities while maintaining minimal computation time. The research shows that the student model effectively learns from the teacher model using the WeedMap dataset, achieving accurate results suitable for mobile platforms such as drones, with only 0.5 GMacs compared to 42.5 GMacs of the teacher model. The trained models obtained an F1 score of 0.863 and 0.631 on two data subsets, with a performance improvement of 2 and 7 points, respectively, over the undistilled model. The study results suggest that developing efficient computer vision algorithms on drones can significantly improve agricultural management practices, leading to greater profitability and environmental sustainability.