Older adults are particularly susceptible to falls following perturbations during standing, such as forward loss of balance. Back support devices that assist trunk extension may help mitigate fall risk by preventing excessive trunk flexion. Previous studies have investigated heavy back support devices; however, these systems often introduced adverse effects on stability due to their added mass, which shifted the body's natural center of mass unfavorably. In contrast, lightweight passive devices have shown limited benefits, as they can generate only modest assistive forces during the relatively small trunk flexion associated with forward balance loss. In this study, we evaluated the effects of a lightweight semi-active soft back support device on postural stability following standing perturbations. Our device combines an active element (a pneumatic artificial muscle) in parallel with a passive elastic band. The active element rapidly provides assistive force following a perturbation, overcoming the limitations of passive devices. Experiments conducted with five healthy individuals demonstrated that the semi-active device significantly reduced whole-body angular momentum and increased the margin of stability, indicating improved balance recovery performance. These results highlight the promise of semi-active soft wearable robots as an effective and lightweight strategy for fall prevention during standing perturbations.