The area of the inside diameter of the tube and the outside diameter of the tube both have a bearing on the ability to resist bending and torsional flexing.More accurately,it depends on area squared and the difference between inside and outside values.IT'S NOT ROCKET SCIENCE OR MAGIC.
*For a given weight of tube,increasing the inside and outside diameters will help rigidity.There is a limit to how far you can go with this;the tube will buckle easily if it becomes thin like a beer can.
*For a given outside diameter,decreasing the I.D. which means INCREASING THE WALL THICKNESS AND WEIGHT,will ALWAYS INCREASE RIGIDITY.