A yeast infection can make birds ravenous and still incessantly beg for food even with a full crop. I would have a vet check to make sure you don't have an issue there, the fact he has already been passed around would cause enough stress to weaken the immune system for this to be a great possibility.
Other than this you have received some great advice, as long as there isn't a medical reason he will wean in his own time.
I think he's making up for not being fed properly. I watched the lady I got him from feed him and she just shot food down his throat really quick and then went to the next baby. That was it. There was no tasting the food, no interaction, nothing. I think being underfed and under socialized for his first 5-6 weeks got him accustomed to begging constantly. He has gained 4 grams in just the past 5 days. I don't suspect a yeast infection because he is properly digesting everything, and gaining weight accordingly. He has no signs of a yeast infection, he's just a fatty.
I will take him to the vet to get him cleared for adoption whenever he is ready. I'm still waiting for his breast bone to get some fat around it. He's a skinny little guy, but like I said he's doing much better. He's nibbling millet and some pellets.
Is he eating anything other than the formula? Also, are you feeding him just plain formula? If so, that could be one reason he is always hungry. When I raised Diva Tiel (beak injury by a lovebird), my vet had me disolve my Harrison's pellets and add them to the formula a little at a time until after two or three months really all she was getting was disolved pellets. It helped her to bridge from formula to pellets; she began refusing the formula flavored food and demanding the Harrisons disolved food. Due to her injury, Diva did not wean until whe was 18 months old. Other tiels with normal beaks usually weaned completely by eight weeks, but I had one that went twelve weeks.
Is he with any other tiels that could show him how to forage from the cage floor? That was another thing that helped Diva finally wean.
He downright refuses anything I offer if it isn't formula. He begs so much that for awhile I could get away with putting wet Harrison's pellets into his mouth and he would chew and swallow and keep begging for formula, eventually he caught on and now only begs with a closed mouth if he thinks I'm up to anything. He is finally starting to pick around at things. There are seeds and pellets all over the bottom of the cage for him to 'forage', he's also playing with his toys A LOT! I still think it'll be at least two or three more weeks before I put the formula and syringes away for good, but progress it progress and I couldn't be happier. I caught him munching on some millet today while talking to my SO, I hushed him and we both watched the baby eat away at his millet. It was a sacred bird mom moment.
Poor guy is still trying to figure out why his wings won't work. It must be hard for their little brains to understand the lack of such an instinctual thing. I think he thinks if he flaps and jumps up enough he will eventually fly.
Oh, and no, no tiels. He is my only tiel.