Accurate crop yield forecasting is essential for global food security. However, current AI models systematically underperform when yields deviate from historical trends. This issue arises from key data challenges, including a major asymmetry between rich pretraining weather datasets and the limited data available for fine-tuning. We introduce VITA (Variational Inference Transformer for Asymmetric data)}, a variational pretraining framework that addresses this asymmetry. Instead of relying on input reconstruction, VITA uses detailed weather variables as proxy targets during pretraining and learns to predict rich atmospheric states through self-supervised feature masking. This allows the model to be fine-tuned using only basic weather statistics during deployment. Applied to 763 counties in the U.S. Corn Belt, VITA achieves state-of-the-art performance in predicting corn and soybean yields across all evaluation scenarios. While it consistently delivers superior performance under normal conditions, its advantages are particularly pronounced during extreme weather years, with statistically significant improvements (paired t-test, $p \approx 0.01$). Importantly, VITA outperforms prior frameworks like GNN-RNN using less data, making it more practical for real-world use—particularly in data-scarce regions. This work highlights how domain-aware AI design can overcome data limitations and support resilient agricultural forecasting in a changing climate.