This paper deals with the problem of informative path planning for a UAV deployed for precision agriculture applications. First, we observe that the ``fear of missing out'' data lead to uniform, conservative scanning policies over the whole agricultural field. Consequently, employing a non-uniform scanning approach can mitigate the expenditure of time in areas with minimal or negligible real value, while ensuring heightened precision in information-dense regions. Turning to the available informative path planning methodologies, we discern that certain methods entail intensive computational requirements, while others necessitate training on an ideal world simulator. To address the aforementioned issues, we propose an active sensing coverage path planning approach, named OverFOMO, that regulates the speed of the UAV in accordance with both the relative quantity of the identified classes, i.e. crops and weeds, and the confidence level of such detections. To identify these instances, a robust Deep Learning segmentation model is deployed. The computational needs of the proposed algorithm are independent of the size of the agricultural field, rendering its applicability on modern UAVs quite straightforward. The proposed algorithm was evaluated with a simu-realistic pipeline, combining data from real UAV missions and the high-fidelity dynamics of AirSim simulator, showcasing its performance improvements over the established state of affairs for this type of missions. An open-source implementation of the algorithm and the evaluation pipeline is also available: \url{https://github.com/emmarapt/OverFOMO}.