When my legs got strong enough to stand to pedal for climbs and sprints, I noticed my balance was terrible. That turned out to be mostly related to the short stems I preferred for comfort while seated.
Switching to longer stems helped with my balance. Lowering the stem a bit helped too. Much more stable, even when I'm in the drops while standing to climb hills.
But that introduced a whole nuther set of challenges, especially neck and back flexibility with the extended reach.