How bad is he when asked to turn right? Has anyone inspected the tree points? What about the flocking? Since it's just with weight and he's fine without, I'm wondering where the rider's seat bones hit. Or do they have a tight thigh that might be pressing something?
I'm still stuck in the fine without weight, but not fine with. I'd want to pinpoint exactly what is up with the addition of weight before spending $$$ on scans. But that reflects my current budget and your client may have a different situation. ;)

