Having been anorexic throughout the whole of high school (in England that's from the age of 11 to 18), I can say you would honestly be surprised at the level of abuse I got for looking the way I did. I won't go into detail, but let's just say the abuse did not simply stop at name-calling and verbal slander; it did get physical.
However, it was not quite on par with the bullying I knew some of my overweight friends suffered at different schools. It was close, but probably only due to the extreme at which my weight sat. Those who were thin without looking ill were certainly not abused over anything as far as I know.
But this is only regarding personal and direct abuse as opposed to society's view of fat people and thin people as a whole. On such a wide scale, I must say that from what I have seen that people who are deemed overweight do suffer worse abuse than those whom society labels as 'thin'.
So I suppose what I'm trying to say is: people who carry more weight are typically subject to worse abuse than than those who are 'thin' by society's standards, however each case is entirely circumstantial to the individual.
Just my two pence-worth