I'm going to echo some other sentiments and urge you to limit the portions of her food. It's tough because there are two birds in the cage and one is okay and the other is obese (and really she is obese if you can't feel her keel). Limiting food intake does include not adding in more veggies in place of the free choice pellets. The 4g weight change you're seeing unfortunately is not a significant change. It could be the difference between a full crop and an empty, or even partially if she just pooped.
How much food are they offered every day? If you had to put a quantity on it.
Getting her to fly is going to be super important, if you can get her to keep flying laps daily that's going to help reduce the fat and build muscle. Hopefully more exercise and the low-cal pellets will help!