In the realistic world, various individuals have distinct personalities, preferences, and attitudes toward new information and behavior acceptance, called population heterogeneity. It is seldom taken into account and theoretically analyzed in information propagation on a weighted network. Therefore, we divide individuals into fashionable and conservative individuals according to their passion degree and willingness for novel behaviors acceptance. Then, we build two behavior adoption threshold models corresponding to fashionable and conservative individuals on the weighted network to explore the effect of population (...) heterogeneity on information propagation. Next, a partition theory based on edge weight and population heterogeneity is proposed to qualitatively analyze the information propagation mechanism. The theoretical analyses and simulation results show that fashionable individuals promote information propagation and behavior adoption. More importantly, the crossover phenomena of phase transition appear. When the fraction of fashionable individuals is relatively large, the increasing pattern of the final adoption size shows a second-order continuous phase transition. In comparison, the increasing pattern alters to first-order discontinuous phase transition with the decrease of the fraction of fashionable individuals. Moreover, reducing weight distribution heterogeneity promotes information propagation and slightly accelerates the change of the phase transition pattern from the first-order discontinuous to the second-order continuous. Besides, increasing the degree distribution heterogeneity accelerates the change of the phase transition pattern. Finally, our theoretical analyses coincide well with the simulation results. (shrink)