The aim of the present paper was to examine the associations between anthropometric parameters, overweight, obesity, and socioeconomic status (SES) of children and adolescents in Poland. Data were collected in the “Elaboration of reference blood pressure ranges for children and adolescents in Poland” OLAF-PL0080 (OLAF) study, a nationally representative survey on growth and blood pressure references for children and adolescents aged 7–18 years. Body height, weight, and waist circumference (WC) were measured, and body mass index (BMI) was calculated. Anthropometric parameters were standardized for age and gender and expressed as z-scores. Statistical analyses were conducted on 10,950 children and adolescents whose parents provided socioeconomic questionnaires. The associations between anthropometric parameters, overweight (including obesity), and SES were analyzed using multiple regression and multiple logistic regression. The height was positively associated with higher levels of maternal education and, in the case of girls, also with paternal education. Higher level of income per capita, but not the highest, was associated with higher weight, BMI, and WC and, in the case of boys, also tall stature. The height, weight, BMI, and waist were significantly inversely associated with number of children in the family. Lower number of children in the family and higher level of income, but not the highest, increased odds of overweight and obesity. In the case of girls, the odds of obesity decreased with paternal higher level of education. Conclusion: The social position associated with parents’ education, better environment, and SES correlate with body height and weight of a child. However, it is associated with higher risk of overweight and abdominal obesity.