Although there is an increasing awareness of the suitability of using compositional data methodology in public health research, classical methods of statistical analysis have been primarily used so far. The present study aims to illustrate the potential of robust statistics to model movement behaviour using Czech adolescent data. We investigated: (1) the inter-relationship between various physical activity (PA) intensities, extended to model relationships by age; and (2) the associations between adolescents’ PA and sedentary behavior (SB) structure and obesity. These research questions were addressed using three different types of compositional regression analysis—compositional covariates, compositional response, and regression between compositional parts. Robust counterparts of classical regression methods were used to lessen the influence of possible outliers. We outlined the differences in both classical and robust methods of compositional data analysis. There was a pattern in Czech adolescents’ movement/non-movement behavior—extensive SB was related to higher amounts of light-intensity PA, and vigorous PA ratios formed the main source of potential aberrant observations; aging is associated with more SB and vigorous PA at the expense of light-intensity PA and moderate-intensity PA. The robust counterparts indicated that they might provide more stable estimates in the presence of outlying observations. The findings suggested that replacing time spent in SB with vigorous PA may be a powerful tool against adolescents’ obesity.