Kernel functions support a broad range of applications that require tasks like density estimation, classification, or outlier detection. In these tasks, a common online operation is to compute the weighted aggregation of kernel function values with respect to a set of points. Scalable aggregation methods are still unknown for typical kernel functions (e.g., Gaussian kernel, polynomial kernel, and sigmoid kernel) and weighting schemes. In this paper, we propose a novel and effective bounding technique to speedup the computation of kernel aggregation. We further boost its efficiency by leveraging index structures and exploiting index tuning opportunities. In addition, our technique is extensible to different types of kernel functions and weightings. Experimental studies on many real datasets reveal that our proposed method achieves speedups of 2.5-738 over the state-of-the-art.