To evaluate association between overweight/obesity and sugar-sweetened beverages (SSB) types, SSB sugar, among children and adolescents. A total of 1,068 children and 751 adolescents were identified from a provincial survey conducted in Shandong, China. χ2 tests, logistic regression, restricted cubic spline (RCS), mediation analysis, pathway analysis, and ordinary least square (OLS) regression were applied to test association among overweight/obesity, SSB sugar, SSB types, and a set of factors. The mean daily SSB intake for children and adolescents was 210.7 and 208 ml, respectively. The threshold of SSB sugar consumption causing overweight/obesity was around 25 g/day and verified by RCS based on logistic regression. Approximately, 44.8% of the study subjects consumed more than 25 g/day of SSB sugar. SSB sugar intake above 25 g/day resulted in higher risk of overweight/obesity (OR = 1.391, 95% CI, 1.115–1.734). The effects of all types of SSBs on overweight/obesity were fully mediated by SSB sugar (p < 0.05), except for milk. Consumption of any types of SSBs had a positive impact on SSB sugar intake in both children and adolescents. Any type of SSB intake was a risk factor in excessive intake of SSB sugar (OR > 1, p < 0.05). In particular, milk powder, tea, and tea-flavored drinks, and carbonated have greater ORs for excessive intake of SSB sugar (OR = 76.08, 8.879, 4.355, p < 0.05, respectively). It was found that the effect of SSB on overweight/obesity was mediated by the intake of SSB sugar, and the effects of various SSBs were different according to multiple linear regression and pathway analysis (p < 0.05, respectively).