Many children suffer from this problem nowadays. Most of these children do not have this problem after about 4 to 5 years of age.
Lot of research has been done about steroids like budecort given with nebulizer or inhaling via other methods, continuously, for a long time time. There are no side-effects.it certainly does not effect mental health.
Yes your child is overweight. It is not due to medicines, because if it was due to medicine, your child will have increased appetite, but you said that he does not have appetite.
You should feed your child only four times in 24 yours.in between he should have two glassses of milk., If he is breast feeding , you should try to stop that now. If he does not want to eat do not force feed him.
As I said before most of these children do not have this problem when they grow up