For a solid circular cross-section, the stiffness (for both bending and torsion) is proportional to the diameter to the fourth power, or D^4. For a tube, the stiffness is proportional to (D^4 - d^4), where small d is the inner diameter.

Here are some examples, using a 1" solid bar as the baseline.

1.000" Bar: 1.000
1.125" Bar: 1.602
1.250" Bar: 2.441

1.25" Tube, 1.00" ID: 1.441
1.25" Tube, 0.75" ID: 2.125
1.50" Tube, 1.25" ID: 2.621
1.50" Tube, 1.00" ID: 4.063

These are just relative stiffnesses. To translate these into actual roll rates would require a lot more calculation. It gets a lot more complicated when you factor in the mounts and bushings. You could look at the mounts as being additional springs in series with the actual sway bar. What this amounts to is that as your bar gets proportionally stiffer, the actual roll stiffness of the car won't increase quite as much, due to the compliance of the mounts/bushings/car itself.

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