Postural stability becomes compromised with advancing age, but the neural mechanisms contributing to instability have not been fully explicated. Accordingly, this quantitative physiological and MRI study of sex differences across the adult age range examined the association between components of postural control and the integrity of brain structure and function under different conditions of sensory input and stance stabilization manipulation. The groups comprised 28 healthy men (age 30–73 years) and 38 healthy women (age 34–74 years), who completed balance platform testing, cognitive assessment, and structural MRI. The results supported the hypothesis that excessive postural sway would be greater in older than younger healthy individuals when standing without sensory or stance aids, and that introduction of such aids would reduce sway in both principal directions (anterior–posterior and medial–lateral) and in both the open-loop and closed-loop components of postural control even in older individuals. Sway reduction with stance stabilization, that is, standing with feet apart, was greater in men than women, probably because older men were less stable than women when standing with their feet together. Greater sway was related to evidence for greater brain structural involutional changes, indexed as ventricular and sulcal enlargement and white matter hyperintensity burden. In women, poorer cognitive test performance related to less sway reduction with the use of sensory aids. Thus, aging men and women were shown to have diminished postural control, associated with cognitive and brain structural involution, in unstable stance conditions and with diminished sensory input.