I don't know if this will make me popular, but I agree with John. I think you will be able to see changes in Matthew, and you don't need to assign him a number. As time goes on he will feel better, and the success will build on itself - and I think if he only loses two pounds in the next month that's still great. He's just baby still, really, and it is awful that he's having to go through this but my heart tells me that making him 'weigh in' will make things worse.
On the other hand, as a kind of compromise, maybe you could make an appointment for a physical with his pediatrician. They would certainly take his weight and other measurements like blood pressure and that type of thing, and then in a year he could have another checkup and see how he's progressed.
I understand wanting to know how much he weighs - my daughter weighs herself almost every day because she sees Mommy do it so much - and probably Matthew is old enough to decide for himself how he wants to track his progress.
It's a toughie - good luck with the decision. I know whatever you decide it will be based on your love for him, so it will be the right choice no matter what.