Best post here. Play on the "paper mage" trope and make lower weights give Int instead of the highest weights. Make the heaviest hitting mages have to really risk their lives in return for power, but still able to keep a solid distance via speed.
To round it out, remove the Int bonus from high weights, give Obese more health than Bulging, and make weight gain above Stout purely a matter of a greater and greater health pool at the cost of Str/Con/Dex/Stam.
On Lean/Fit/Stout, I think their current balance is just fine. Further modification past the above would just lead to a different weight class replacing Stout as the standard, which just moves this thread from "Why can I only play Stout?" to "Why can I only play Fit/Lean/etc.?"
Better off just looking at why specific races aren't doing well/are doing too well and solving it at the source than trying to fix racial balance by changing things that impact all races. That just leads to most races being in the unusable bin like we had in Mortal Online (1).
Getting rid of int/psyche bonuses for bulging/obese recreates the same problem facing skinny/bony, just on the other end. Without the int, nobody would ever go obese or bulging. The int bonuses (but not necessarily the psyche, since lower weights also get a dex bonus) should be the same for both groups. This allows for more than 1 pure mage play style. You can either go the tanky, high hp nuker or the speedy, avoidance-based nuker.
All weight classes need to have viability, but right now they do not. Relatedly, they should just abolish skeletal.