Pupillometry has been used in the studies of postural control to assess cognitive load during dual tasks, but its response to increased balance task intensity has not been investigated. Furthermore, it is unknown whether side-specific changes in pupil diameter occur with more demanding balance tasks providing additional insights into postural control. The two aims of this study were to analyze differences in steady-state pupil diameter between balance tasks with increased intensity and to determine whether there are side-specific changes. Forty-eight healthy subjects performed parallel and left and right one-legged stances on a force plate with and without foam with right and left pupil diameters measured with a mobile infrared eye-tracker. Differences between balance tasks in parameters (average pupil diameter of each eye, average of both pupil diameters and the difference between the left and right pupil diameter) were analyzed using a two-way repeated measures analysis of variance, and deep learning neural network models were used to investigate how pupillometry predicted each balance task. The pupil diameter of the left eye, the average pupil diameter of both eyes and the difference in pupil diameters increased statistically significantly from simpler to more demanding balance tasks, with this being more pronounced for the left eye. The deep learning neural network models revealed side-specific changes in pupil diameter with more demanding balance tasks. This study confirms pupillary responses to increased intensity of balance task and indicates side-specific pupil responses that could be related to task-specific involvement of higher levels of postural control.