Down syndrome (DS), caused by the triplication of chromosome 21 (T21), is a prevalent genetic disorder with a higher incidence of obesity. Traditional approaches have struggled to differentiate T21-specific molecular dysregulation from general obesity-related processes. This study introduces the omni-PLIER framework, combining the Pathway-Level Information ExtractoR (PLIER) with the omnigenic model, to uncover molecular mechanisms underlying obesity in DS. The PLIER framework aligns gene expression data with biological pathways, facilitating the identification of relevant molecular patterns. Using RNA sequencing data from the Human Trisome Project, omni-PLIER identified latent variables (LVs) significantly associated with both T21 and body mass index (BMI). Elastic net regression and causal mediation analysis revealed LVs mediating the effect of karyotype on BMI. Notably, LVs involving glutathione peroxidase-1 (GPX1) and MCL1 apoptosis regulator, BCL2 family members emerged as crucial mediators. These findings provide insights into the molecular interplay between DS and obesity. The omni-PLIER model offers a robust methodological advancement for dissecting complex genetic disorders, with implications for understanding obesity-related processes in both DS and the general population.