And your "means tested thin benefit". What about people with glandular disorders? For instance, hypothyroidism cause obesity which can lead to diabetes, but the person with it (myself, for instance) has no control over it until a doctor finally recognizes it, and then it is still impossible to get the weight off, just control the other issues like the headaches and mood swings. Any benefit must be applied equally, so are we going to allow benefits ot those with doctor's notes certifying their condition is beyond their control? And who is going to make the judgment? I'm 5'11". Most stats say I should weigh 160, but the doctor says, with my 34" shoulders, 200 is a better target for me. So I'm about 20% over weight at 240, but with a medical condition where I can't lose weight.
And I'm not that uncommon when it comes to thyroid issues and diabetes. In fact, my doctor says I'm doing good to maintain the 240-250 that I do (I go up a bit in the winter).