While there is significant attention aimed at understanding how one-dimensional confinement and chain confirmations can impact the glass transition temperature (Tg) of polymer films, there remains a limited focus on similar effects on sub-Tg processes, notably, structural relaxation. Using spectroscopic ellipsometry, we investigated the combined influence of confinement and molecular packing on Tg and physical aging, i.e., the property changes that accompany structural relaxation, at select film thicknesses and aging temperatures (Ta). We used poly(methyl methacrylate) (PMMA) films in the brush and spin-coated morphologies as model systems. We found that whether a PMMA film exhibited a decrease or increase in physical aging rate with confinement was dependent on the morphology. Notably, PMMA brushes exhibited higher physical aging rates compared to similarly thick spin-coated films at all values of Ta. These intriguing findings reveal the strong effects of confinement and molecular packing on the structural relaxation of polymer films. Results from this study have the potential to aid in the design of thin-film materials with controllable long-term glassy-state properties.