Electric load forecasting is essential for power management and stability in smart grids. This is mainly achieved via advanced metering infrastructure, where smart meters (SMs) are used to record household energy consumption. Traditional machine learning (ML) methods are often employed for load forecasting but require data sharing which raises data privacy concerns. Federated learning (FL) can address this issue by running distributed ML models at local SMs without data exchange. However, current FL-based approaches struggle to achieve efficient load forecasting due to imbalanced data distribution across heterogeneous SMs. This paper presents a novel personalized federated learning (PFL) method to load prediction under non-independent and identically distributed (non-IID) metering data settings. Specifically, we introduce meta-learning, where the learning rates are manipulated using the meta-learning idea to maximize the gradient for each client in each global round. Clients with varying processing capacities, data sizes, and batch sizes can participate in global model aggregation and improve their local load forecasting via personalized learning. Simulation results show that our approach outperforms state-of-the-art ML and FL methods in terms of better load forecasting accuracy.