Support Vector Regression (SVR) is a powerful method for regression tasks, but it suffers from high computational complexity and sensitivity to outliers. Several implementations of Granular Ball based SVR have been introduced to improve efficiency by summarizing data using granular balls which are a compact representations of data distributions. However, these implementations treat all granular balls equally, disregarding variations in their densities and importance. To address this, we propose Adaptive Weighted Granular Ball Support Vector Regression (AW-GBSVR), which assigns asymmetric weights to granular balls based on their statistical properties. This allows the model to prioritize more informative granular balls while reducing the influence of noisy or less significant ones. The proposed model is evaluated against recent granular ball based algorithms on benchmark and time-series datasets, demonstrating superior performance.