Autonomous robotic weeding in grasslands requires robust weed segmentation. Deep learning models can provide solutions to this problem, but they need to be trained on large amounts of images, which in the case of grasslands are notoriously difficult to obtain and manually annotate. In this work we introduce Few-leaf Learning, a concept that facilitates the training of accurate weed segmentation models and can lead to easier generation of weed segmentation datasets with minimal human annotation effort. Our approach builds upon the fact that each plant species within the same field has relatively uniform visual characteristics due to similar environmental influences. Thus, we can train a field-and-day-specific weed segmentation model on synthetic training data stemming from just a handful of annotated weed leaves. We demonstrate the efficacy of our approach for different fields and for two common grassland weeds: Rumex obtusifolius (broad-leaved dock) and Cirsium vulgare (spear thistle). Our code is publicly available at https://github.com/RGring/WeedAnnotator.