Graphs are widely used to model the relational structure of data, and the research of graph machine learning (ML) has a wide spectrum of applications ranging from drug design in molecular graphs to friendship recommendation in social networks. Prevailing approaches for graph ML typically require abundant labeled instances in achieving satisfactory results, which is commonly infeasible in real-world scenarios since labeled data for newly emerged concepts (e.g., new categorizations of nodes) on graphs is limited. Though meta-learning has been applied to different few-shot graph learning problems, most existing efforts predominately assume that all the data from those seen classes is gold-labeled, while those methods may lose their efficacy when the seen data is weakly-labeled with severe label noise. As such, we aim to investigate a novel problem of weakly-supervised graph meta-learning for improving the model robustness in terms of knowledge transfer. To achieve this goal, we propose a new graph meta-learning framework -- Graph Hallucination Networks (Meta-GHN) in this paper. Based on a new robustness-enhanced episodic training, Meta-GHN is meta-learned to hallucinate clean node representations from weakly-labeled data and extracts highly transferable meta-knowledge, which enables the model to quickly adapt to unseen tasks with few labeled instances. Extensive experiments demonstrate the superiority of Meta-GHN over existing graph meta-learning studies on the task of weakly-supervised few-shot node classification.