With the rapid development of science technology, finding prevalent spatial patterns from urban facility data has gradually become an important issue in smart city applications. Co-location pattern mining is a valid method for identifying patterns whose instances are prevalent in geographical proximity. However, existing methods treat the space as homogeneous and non-directional, and both the proximity levels and connecting directions of instances are neglected during the mining process, causing the minded patterns to be unsatisfactory. Tobler's First Law indicates that the contributions of instances to their pattern's significance diminish as the distance decreases. Moreover, the directions in which instances are connected should also be considered due to the distance decay effects. Following these threads, this paper proposes a novel co-location pattern mining algorithm mixed with a density-weighted distance thresholding consideration. Based on the framework of our previous SGCT algorithm, which concentrates on efficiency and storage issues, this solution comprises an extension called SGCT-K, which is mainly concerned with improving the effectiveness of the mined results. It adopts a kernel-density-estimation-based model to measure the proximity level of different instance types and respects their directions during the instance connecting process. We implement experiments using both synthetic and real-facility datasets in Beijing, China. The results provide sound evidence that the algorithm improves both accuracy and sensitivity compared to previous methods.