Everything is going to hinge on the Honorable discharge. You'll get education benefits under the Post 9/11 GI Bill (chapter 33) if you get the Honorable. I'm not sure what the criteria is to get the Honorable, but it seems to me about one half of the folks with a weight control failure do get an Honorable. MGIB chapter 30 benefits will probably be a no go for you though. Depends on how many months your original contract was for and how many months you finished. If your weight control failure was chapter 18, then you need to serve 20 months of a 24 month emlistment or 30 months of an enlistment of 3 years or longer. If not under chapter 18 then you'll need to finish 24 months on a 2 year contract and 36 months if your contract is 3 or more years. BUT, everything will be decided based on your honorable discharge. In your case, no honorable, no benies.
Sounds like it is totally going to be on what kind of discharge you get. at this point if you get an honrable you'll get benefits...if not, you will not. At that point seek advice on getting your discharge upgraded.