Nobody who fat shames has shown me research about the efficacy of fat shaming on weight reduction. That's not necessarily because the research doesn't exist, it's because they just don't care.
Nobody wants to be fat and most are already pretty ashamed about it. The big over-eaters (like myself) are sort of like addicts, but its a drug we really can't quit. It's like trying to manage your alcoholism by drinking 2 drinks a day instead of 10.
It's easy to think "why doesn't the pig just eat less." I used to think that way until my diagnosed thyroid conditions (which made me skinny by default) was treated. Karma.
Though some fat acceptance groups go too far when they criticize doctors for telling them to lose weight.