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This sounds like separation anxiety.
He is letting you know he is anxious / distressed when someone leaves.
Have a read here:
Some dogs dislike being left alone while others dislike anyone leaving; both scenarios can be classed as 'separation anxiety'.
As he is on a diet, consider giving his regular meals inside food puzzles, so they take more time for him to get through.
Low calorie options include raw carrot, cottage cheese, raw apple and perhaps a small amount of protein such as chicken or white fish. Peanut butter works well for smearing but is high in calories.
Hopefully this is useful!