The state-of-the-art recommendation systems have shifted the attention to efficient recommendation, e.g., on-device recommendation, under memory constraints. To this end, the existing methods either focused on the lightweight embeddings for both users and items, or involved on-device systems enjoying the compact embeddings to enhance reusability and reduces space complexity. However, they focus solely on the coarse granularity of embedding, while overlook the fine-grained semantic nuances, to adversarially downgrade the efficacy of meta-embeddings in capturing the intricate relationship over both user and item, consequently resulting into the suboptimal recommendations. In this paper, we aim to study how the meta-embedding can efficiently learn varied grained semantics, together with how the fine-grained meta-embedding can strengthen the representation of coarse-grained meta-embedding. To answer these questions, we develop a novel graph neural networks (GNNs) based recommender where each user and item serves as the node, linked directly to coarse-grained virtual nodes and indirectly to fine-grained virtual nodes, ensuring different grained semantic learning, while disclosing: 1) In contrast to coarse-grained semantics, fine-grained semantics are well captured through sparse meta-embeddings, which adaptively 2) balance the embedding uniqueness and memory constraint. Additionally, the initialization method come up upon SparsePCA, along with a soft thresholding activation function to render the sparseness of the meta-embeddings. We propose a weight bridging update strategy that focuses on matching each coarse-grained meta-embedding with several fine-grained meta-embeddings based on the users/items' semantics. Extensive experiments substantiate our method's superiority over existing baselines. Our code is available at https://github.com/htyjers/C2F-MetaEmbed.