Non-rigidly foldable origamis are of great interest to build robotic components, as they are light, offer large deployability and can also be multistable. In this paper, we consider the Kresling tower, and propose an original way to actively modulate its kinetostatic properties. Actuated stiffening mechanisms are embedded on some folds of the origami. By adjusting the axial stiffness of the folds, modulation of the axial stiffness and the force required to switch between stable configurations are demonstrated. This adjustment can in addition be performed independently from the height of the stable configurations, which makes it simple to use. The interest of fold stiffening is outlined experimentally. Three actuation strategies are considered and implemented. Impact on Kresling tower properties are shown, with complementary performances of pneumatic, SMA-based and DC motor actuation.