The vagal blockage is a surgically implanted device that sends electrical signals to your abdominal vagus nerve which reduces your hunger.
There was one trial on this of reasonable quality of ~240 people. One group had the vagal device and the other had a fake device. After 12 months, patients in the active vagal device group lost more weight. For example, if all the people started at 100kg, then those with a fake device lost ~6kg versus those with a real vagal device lost 9kg. So about a 3kg difference if your start weight was 100kg after 12 months.
The most common side effects were heartburn and abdominal pain.