On a one-handed, non-versatile weapon, the small property has no particular function, except to qualify the weapon for certain feats or other effects requiring the small property.
Small characters cannot normally wield two-handed weapons. Small characters can wield a shortbow, however, because the shortbow has the small property.
Small characters are normally required to wield versatile weapons with two hands, and receive no bonus for doing so. Small characters may wield a lance either one- or two-handed, however, and receive a bonus for wielding it two-handed, because the lance has the small property.