Part of the problem is that we are, and look set to remain, a 'fattist' society.
Look at the adjectives there are to describe obese people - I won't quote any here, but suffice to say, there is probably twenty for every one to refer to an unusually thin person.
That means that the default reaction to an obese person is that they are greedy, and can help themselves, but won't, whereas anorexia is firmly aligned with mental illness, resulting in sympathy from society at large.
Until we adjust our attitudes to the causes of both these distressing conditions, the inequality in terms of wider sympathy will continue.