You can do it in Karamba. Set both the in plane and out of plane shell stiffnesses to very small values. Reverse gravity then run a large deformation analysis and scale the reverse gravity force to alter the shell geometry. You then use the deformed geometry as an input to a second stage Karamba analysis with real material properties to calculate shell stresses. Google Karamba form finding, there are examples

If the change between starting and form-found geometry is small, then you can simply assign loads proportional to mesh triangle areas at the start.

However, if you mean particularly modifying the self weight iteratively according to the way the area changes during form-finding, then I can share a goal to do this. There is already one in there to modify weights based on lengths, but it is a simple matter to extend this to triangle areas. When I've tried this in the past though the difference in resulting geometry is usually tiny.