It seems you are transferring your own negative experience with a doctor(s) onto them all. You have said your brother sees professional help for other reasons. These doctors may be treating these issues as the ones needing primary attention. Besides, you don't go to his sessions so how are you so sure to know that his weight and possible health issues have not been discussed and broached? A psychiatrist is still a medical doctor. If he is concerned he would have referred your brother to seek medical attention. Incidentally, is your brother on medication. Most psychiatric medications require regular blood tests. His psychiatrist would order a round of them with a broader scope including those that would indicate further testing was required for diabetes. No, I trust he is in good hands.

As for your mother, it does sound like there might be a co-dependent relationship. But that is theirs and not yours to solve. You have spoken apparently repeatedly to your mom. Leave it at that. What you might be able to do is to encourage her to get help as a support person - like attending a support for caregivers of the mentally ill.