Sugar intake has been associated with increased prevalence of childhood overweight/obesity; however, results remain controversial. The aim of this study was to examine the probability of overweight/obesity with higher sugar intakes, accounting for other dietary intakes. Data from 1165 children and adolescents aged ≥2–18 years (66.8% males) enrolled in the Hellenic National Nutrition and Health Survey (HNNHS) were used; specifically, 781 children aged 2–11 years and 384 adolescents 12–18 years. Total and added sugar intake were assessed using two 24 h recalls (24 hR). Foods were categorized into specific food groups to evaluate the main foods contributing to intakes. A significant proportion of children (18.7%) and adolescents (24.5%) exceeded the recommended cut-off of 10% of total energy intake from added sugars. Sweets (29.8%) and processed/refined grains and cereals (19.1%) were the main sources of added sugars in both age groups, while in adolescents, the third main contributor was sugar-sweetened beverages (20.6%). Being overweight or obese was 2.57 (p = 0.002) and 1.77 (p = 0.047) times more likely for intakes ≥10% of total energy from added sugars compared to less <10%, when accounting for food groups and macronutrient intakes, respectively. The predicted probability of becoming obese was also significant with higher total and added-sugar consumption. We conclude that high consumption of added sugars increased the probability for overweight/obesity among youth, irrespectively of other dietary or macronutrient intakes.