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Crop field boundaries aid in mapping crop types, predicting yields, and delivering field-scale analytics to farmers. Recent years have seen the successful application of deep learning to delineating field boundaries in industrial agricultural systems, but field boundary datasets remain missing in smallholder systems due to (1) small fields that require high resolution satellite imagery to delineate and (2) a lack of ground labels for model training and validation. In this work, we combine transfer learning and weak supervision to overcome these challenges, and we demonstrate the methods' success in India where we efficiently generated 10,000 new field labels. Our best model uses 1.5m resolution Airbus SPOT imagery as input, pre-trains a state-of-the-art neural network on France field boundaries, and fine-tunes on India labels to achieve a median Intersection over Union (IoU) of 0.86 in India. If using 4.8m resolution PlanetScope imagery instead, the best model achieves a median IoU of 0.72. Experiments also show that pre-training in France reduces the number of India field labels needed to achieve a given performance level by as much as $20\times$ when datasets are small. These findings suggest our method is a scalable approach for delineating crop fields in regions of the world that currently lack field boundary datasets. We publicly release the 10,000 labels and delineation model to facilitate the creation of field boundary maps and new methods by the community.