Barred Rocks are bred to be worth butchering, not to be fat. Only CornishX and other commercial meat crosses are bred to get so large they cant move
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THIS. I was going to suggest it, but will finish reading the thread before jumping in.Does she want to roost? You could try making a ramp up to the roost for her.
Can you give her exercise in another other way? Anything?
The excessive fat has to have a source...
How big is the run?
What do you feed?
What is on the floor of the run for litter? Is it fall where you live? My flock will stay very busy if I bring in a bunch of leaves to scratch through. They also go CRAZY for a 50-pound bag of rice hulls. They will scratch in it all day long, and even choose the rice hulls over free ranging. They might be finding bits of rice in there, though, which might not be great for fat. Can you hang some shiny things to peck at?
I'm sure she would have fun scratching in that.