Monitoring species-specific dry herbage biomass is an important aspect of pasture-based milk production systems. Being aware of the herbage biomass in the field enables farmers to manage surpluses and deficits in herbage supply, as well as using targeted nitrogen fertilization when necessary. Deep learning for computer vision is a powerful tool in this context as it can accurately estimate the dry biomass of a herbage parcel using images of the grass canopy taken using a portable device. However, the performance of deep learning comes at the cost of an extensive, and in this case destructive, data gathering process. Since accurate species-specific biomass estimation is labor intensive and destructive for the herbage parcel, we propose in this paper to study low supervision approaches to dry biomass estimation using computer vision. Our contributions include: a synthetic data generation algorithm to generate data for a herbage height aware semantic segmentation task, an automatic pro- cess to label data using semantic segmentation maps, and a robust regression network trained to predict dry biomass using approximate biomass labels and a small trusted dataset with gold standard labels. We design our approach on a herbage mass estimation dataset collected in Ireland and also report state-of-the-art results on the publicly released Grass-Clover biomass estimation dataset from Denmark. Our code is available at https://git.io/J0L2a.