Seagrass meadows serve as critical carbon sinks, but accurately estimating the amount of carbon they store requires knowledge of the seagrass species present. Using underwater and surface vehicles equipped with machine learning algorithms can help to accurately estimate the composition and extent of seagrass meadows at scale. However, previous approaches for seagrass detection and classification have required full supervision from patch-level labels. In this paper, we reframe seagrass classification as a weakly supervised coarse segmentation problem where image-level labels are used during training (25 times fewer labels compared to patch-level labeling) and patch-level outputs are obtained at inference time. To this end, we introduce SeaFeats, an architecture that uses unsupervised contrastive pretraining and feature similarity to separate background and seagrass patches, and SeaCLIP, a model that showcases the effectiveness of large language models as a supervisory signal in domain-specific applications. We demonstrate that an ensemble of SeaFeats and SeaCLIP leads to highly robust performance, with SeaCLIP conservatively predicting the background class to avoid false seagrass misclassifications in blurry or dark patches. Our method outperforms previous approaches that require patch-level labels on the multi-species 'DeepSeagrass' dataset by 6.8% (absolute) for the class-weighted F1 score, and by 12.1% (absolute) F1 score for seagrass presence/absence on the 'Global Wetlands' dataset. We also present two case studies for real-world deployment: outlier detection on the Global Wetlands dataset, and application of our method on imagery collected by FloatyBoat, an autonomous surface vehicle.