Extreme events are of great importance since they often represent impactive occurrences. For instance, in terms of climate and weather, extreme events might be major storms, floods, extreme heat or cold waves, and more. However, they are often located at the tail of the data distribution. Consequently, accurately predicting these extreme events is challenging due to their rarity and irregularity. Prior studies have also referred to this as the out-of-distribution (OOD) problem, which occurs when the distribution of the test data is substantially different from that used for training. In this work, we propose two strategies, reweighting and fine-tuning, to tackle the challenge. Reweighting is a strategy used to force machine learning models to focus on extreme events, which is achieved by a weighted loss function that assigns greater penalties to the prediction errors for the extreme samples relative to those on the remainder of the data. Unlike previous intuitive reweighting methods based on simple heuristics of data distribution, we employ meta-learning to dynamically optimize these penalty weights. To further boost the performance on extreme samples, we start from the reweighted models and fine-tune them using only rare extreme samples. Through extensive experiments on multiple data sets, we empirically validate that our meta-learning-based reweighting outperforms existing heuristic ones, and the fine-tuning strategy can further increase the model performance. More importantly, these two strategies are model-agnostic, which can be implemented on any type of neural network for time series forecasting. The open-sourced code is available at \url{https://github.com/JimengShi/ReFine}.