A weighted pulse decomposition analysis is proposed for cuffless blood pressure assessment. Five Gaussian waves are used for decomposition. The weighted least squares criterion is adopted for optimization. Instead of applying weights to certain crest and trough points of the pulse signal from fingertip photoplethysmogram, we apply the weights to the pulse segment that is recognized informative for vascular age, vessel stiffness, and blood pressure. In addition, the boundary constraints of the Gaussian parameters are carefully set so that the normalized root mean square error (NRMSE) between the original PPG and synthesized PPG can be kept acceptable. From the results, we can see that weighting makes the decomposition stable and the variances of Gaussian parameters reduced. Besides, the modified boundary constraints improve the NRMSE. Furthermore, the correlation between the blood pressures and the features from weighted pulse decomposition analysis is enhanced and thus the proposed approach is helpful to blood pressure assessment.