Synthetic data augmentation via Large Language Models (LLMs) allows researchers to leverage additional training data, thus enhancing the performance of downstream tasks, especially when real-world data is scarce. However, the generated data can deviate from the real-world data, and this misalignment can bring about deficient results while applying the trained model to applications. Therefore, we proposed efficient weighted-loss approaches to align synthetic data with real-world distribution by emphasizing high-quality and diversified data generated by LLMs using merely a tiny amount of real-world data. We empirically assessed the effectiveness of our methods on multiple text classification tasks, and the results showed that leveraging our approaches on a BERT-level model robustly outperformed standard cross-entropy and other data weighting approaches, providing potential solutions to effectively leveraging synthetic data from any suitable data generator.