Effective weed monitoring is a critical component of precision agriculture, directly impacting crop health and yield. This study presents UKANWeed, an application-specific adaptation of the recently proposed UKAN architecture, designed for image segmentation in agricultural settings. UKANWeed integrates Kolmogorov-Arnold Networks (KAN) into its layers, resulting in a lightweight yet highly efficient model that can distinguish weeds from crops. Evaluated on the WeedMap dataset, UKANWeed achieves an F1-score of 86.3, outperforming the widely used UNet architecture while requiring significantly fewer parameters. Additionally, we investigated the behavior of UKANWeed and UNet under extreme model compression, revealing a lower bound in the representational capacity below which task performance degrades sharply. The compactness and accuracy of UKANWeed make it suitable for deployment on edge devices such as drones, enabling real-time, in-field weed detection and crop monitoring—an essential step toward scalable, autonomous precision agriculture. The code is available at https://github.com/pasqualedem/UKANWeed .