Visually guided weight shifting is widely employed in balance rehabilitation, but the underlying visuo-motor integration process leading to balance improvement is still unclear. In this study, we investigated the role of center of pressure (CoP) feedback on the entrainment of active voluntary sway to a moving visual target and on sway’s dynamic stability as a function of target predictability. Fifteen young and healthy adult volunteers (height 175 ± 7 cm, body mass 69 ± 12 kg, age 32 ± 5 years) tracked a vertically moving visual target by shifting their body weight antero-posteriorly under two target motion and feedback conditions, namely, predictable and less predictable target motion, with or without visual CoP feedback. Results revealed lower coherence, less gain, and longer phase lag when tracking the less predictable compared to the predictable target motion. Feedback did not affect CoP-target coherence, but feedback removal resulted in greater target overshooting and a shorter phase lag when tracking the less predictable target. These adaptations did not affect the dynamic stability of voluntary sway. It was concluded that CoP feedback improves spatial perception at the cost of time delays, particularly when tracking a less predictable moving target.