The integration of multiple Global Navigation Satellite Systems (GNSSs), such as the Chinese BeiDou Navigation Satellite System (BDS) and the American Global Positioning System (GPS), makes it possible to improve the accuracy of single-point positioning (SPP). However, the current accuracy of GNSS SPP with code measurement is on the order of several meters. In order to further improve SPP accuracy, we develop a multistep weighted least squares (MWLS) estimation method based on the elevation-dependent weighted least squares (EWLS) method. In this approach, the weight of each visible satellite is determined by its elevation and azimuth, and the coordinate components are semi-independently and separately calculated by MWLS. We conduct open-sky and blocked static tests as well as a vehicle-based kinematic test using single-frequency receivers to assess the effectiveness of this approach. Comparing the positioning errors of GPS and GPS/BDS SPPs between the MWLS and EWLS methods shows that the former improved the positioning accuracy more than the customary latter. Specifically, MWLS achieves a horizontal accuracy of about 1 m and a positional accuracy of 2 to 3 m in clear observational environments, about 15% better than ELWS.