As far as weak minded goes, starving yourself is no easy task. Unfortunately eating is part of living, you take that away and your body freaks out and forces you to eat. If a person can force their cognitive thought process and turn off their Feed/Breath reflex, I'd say thats pretty strong minded.
plus eating disorders stem from another mental illness like schizophrenia (high level of anxiety, not hearing voices) which affects 6% of the worlds population
what you seem to fail to realize is that many people with eating disorders ARE getting help, but, as with depression/addictions/etc, it takes a lot more than a quick visit to the doctor and telling yourself that you'll get better. It takes far more work and time than that.
Also, good for you for taking the healthy path. But if you have low self esteem and are trying to fix it by getting better; thats all it is. Whereas they have something completely different going on in their head.
however celebrities can have eating disorders all they want, as people do actually care what they look like.