Accurate identification of weeds plays a crucial role in helping farmers achieve efficient agricultural practices. An edge-cloud infrastructure can provide efficient resources for weed detection in resource-constrained rural areas. However, deployed applications in these areas often face challenges such as connectivity failures and network issues that affect their quality of service (QoS). We introduce a signal quality-aware framework for precision agriculture that allocates weed inference tasks to resource nodes based on the current network connectivity and quality. Two Machine Learning (ML) models based on ResNet-50 and MobileNetV2 are trained using the publicly available DeepWeeds image classification dataset. A rule-based approximation algorithm is formulated to execute tasks on resourceconstrained computational nodes. We also designed a testbed setup consisting of Raspberry Pi (RPi), personal laptop, cloud server and Parsl environment for evaluating the framework. Reliability of the framework is tested in a controlled setting, under various dynamically injected faults. Experimental results demonstrate that the proposed setup can accurately identify weeds while ensuring high fault tolerance and low completion time, making it a promising solution for weed management in rural agriculture.