Weeds compete with crops for light, water, and nutrients, reducing yield and crop quality. Efficient weed detection is essential for site-specific weed management (SSWM). Although deep learning models have been deployed on UAV-based edge systems, a systematic understanding of how different model architectures perform under real-world resource constraints is still lacking. To address this gap, this study proposes a deployment-oriented framework for real-time UAV-based weed detection on resource-constrained edge platforms. The framework integrates UAV data acquisition, model development, and on-device inference, with a focus on balancing detection accuracy and computational efficiency. A diverse set of state-of-the-art object detection models is evaluated, including convolution-based YOLO models (v8-v12) and transformer-based RT-DETR models (v1-v2). Experiments on three edge devices (Jetson Orin Nano, Jetson AGX Xavier, and Jetson AGX Orin) demonstrate clear trade-offs between accuracy and inference latency across models and hardware configurations. Results show that high-capacity models achieve up to 86.9% mAP50 but suffer from high latency, limiting real-time deployment. In contrast, lightweight models achieve 66%-71% mAP50 with significantly lower latency, enabling real-time performance. Among all models, RT-DETRv2-R50-M achieves competitive accuracy (79% mAP50) with improved efficiency, while YOLOv10n provides the fastest inference speed. YOLOv11s and RT-DETRv2-R50-M offer the best balance between accuracy and speed, making them strong candidates for real-time UAV deployment.