Knowledge Graph Embedding (KGE) aims to project entities and relations into a low-dimensional space, so as to enable Knowledge Graphs (KGs) to be effectively used by downstream AI tasks. Most existing KGs (e.g. Wikidata) suffer from the data imbalance issue, i.e., the occurrence frequencies vary significantly among different entities. Current KGE models use a fixed embedding size, leading to overfitting for low-frequency entities and underfitting for high-frequency ones. A simple method is to manually set embedding sizes based on frequency, but this is not feasible due to the complexity and the large number of entities. To this end, we propose CustomizE, which customizes embedding sizes in a data-driven way, assigning larger sizes for high-frequency entities and smaller sizes for low-frequency ones. We use bilevel optimization for stable learning of representations and sizes. It is noteworthy that our framework is universal and flexible, which is suitable for various KGE models. Experiments on link prediction tasks show its superiority over state-of-the-art baselines.