I'll preface this my saying that there is a child in my wider family with huge weight issues (also tall) and this all sounds very familiar.
Sadly, concern for my relative has torn our wider family apart as everyone has fallen out over it. Those concerned for his welfare haven't been listened to, and it's been a decade long shit-show. We are still on good terms with the child's parents (and in the minority there) but I'm reading your posts saying 'he eats hardly anything' with a good dose of scepticism.
'He eats a few bites here, a few there' isn't good enough if he's two stone overweight at 5. Perhaps he's overeating, perhaps he has a metabolic disorder- either way you MUST pay attention to everything he is eating. My Fitness Pal is great for recording everything he puts in his mouth. Weigh the food, make the effort to document it over a prolonged period. Regardless of where the issue lies you need to do this- you'll either see that he's actually consuming more calories than you thought, OR you'll have the evidence you need to have a metabolic disorder properly investigated.
The child in our family 'ate nothing' too (he ate way too much, but his parents and grandparents didn't and wouldn't see it) and he's been diagnosed with a genetic illness that increases hunger and affects metabolism. His genetic diagnosis has given family members an 'excuse', as though it can't be helped... so he continues to 'eat nothing' (he eats LOADS).
We all have different metabolisms, and we all have to cut our cloth accordingly, if we are to avoid being unhealthily over or under weight.
The best thing you can do right now is to put effort into recording every bite that goes into his mouth, and go from there.