Obesity is a very common problem in corgis. You mention just how hard they will plead to have one more morsel of food. Time to harden your heart just a bit. In rescue I would say that near 60% of the dogs that come in our program are overweight. Most often the problem lies in too much food and not enough exercise. I am typically not a believer is diet foods but changing the ration to be more appropriate for the dog. Many people do reduce the amount of kibble and add green beans. This has worked for many. Make sure that you lose a low sodium or well rinsed product. Many dogs love them. Good luck!