As 'devil's advocate' here, what advantage would that bring?
Most designers would use ASME method (UG-23(b)) (or similar method) to determine the allowable compressive stress in the skirt; the allowable stress is a function of the diameter and nominal thickness (but not, surprisingly, length). In your case the load is essentially the same in both sections of the skirt (slight difference due to the additional weight of the skirt acting at the bottom). So what gain is there to make the different thicknesses? There may be some for functional or other reasons, but there appears to be no structural benefit.
However, sometimes the skirt section may be made of different material at the top of the skirt where the higher vessel temperature exists or if vessel is expensive material, eg: stainless, etc., then use a carbon steel skirt.
This latter point does give some credence to changing the thickness: Where the skirt temperature is high, you might use thicker material in order to keep the allowable stress higher. Where temperature is lower you could use thinner material but maintain similar allowable stress. But I doubt this is done very often in actual practice.