short stature and obesity needs a workup but also keep in mind that we have to take into account just as you said family history, how tall are the biological parents, but also is there an inherited thyroid problem or other concern. If he is very short for age let his pediatrician decide about referral to a pediatric endocrinologist, true fighting the genetic tendency towards obesity is hard but keeping them from gaining weight rapidly is something achieveable, remove all sugared drinks from your home, no soda, no juice, no sweet tea and only have water and low fat milk, no chocolate milk
take away simple sugars and increase fruits and vegetables and increase activity to a daily event. Increase fiber and protein in their diet and have each take a multivitamin with iron and drink much more water than they are.
You are doing your best and a good mom to all by adopting them. Genetic workup will be decided at the time that the doc sees him. Unlikely that there is one cause for this though.
Enuresis and encopresis could be caused by psychological factors such as phobias and anxiety. In your case though they are present for a long time, thus the case of predisposition as a 'triggering' factor still remains. I would recommend a WISC test from a qualified child psychologist and screening for learning difficulties. Wish you the best.