Heterogeneous graph contrastive learning has received wide attention recently. Some existing methods use meta-paths, which are sequences of object types that capture semantic relationships between objects, to construct contrastive views. However, most of them ignore the rich meta-path context information that describes how two objects are connected by meta-paths. On the other hand, they fail to distinguish hard negatives from false negatives, which could adversely affect the model performance. To address the problems, we propose MEOW, a heterogeneous graph contrastive learning model that considers both meta-path contexts and weighted negative samples. Specifically, MEOW constructs a coarse view and a fine-grained view for contrast. The former reflects which objects are connected by meta-paths, while the latter uses meta-path contexts and characterizes the details on how the objects are connected. We take node embeddings in the coarse view as anchors, and construct positive and negative samples from the fine-grained view. Further, to distinguish hard negatives from false negatives, we learn weights of negative samples based on node clustering. We also use prototypical contrastive learning to pull close embeddings of nodes in the same cluster. Finally, we conduct extensive experiments to show the superiority of MEOW against other state-of-the-art methods.