Q: Can you be chaptered out of the military for weight and still get benefits, if you have done an eight-year commitment?
A: I'm going to break your question down into two answers. To begin with, yes, you can be chaptered out of the military for weight under Chapter 18. Why? Because you are in violation of a regulation.
Separation from service is usually at the end of a long road, where the soldier has had multiple opportunities to trim down and make weight, including multiple weigh-ins, medical counseling, remedial physical training, etc. Most commanders will give a soldier every break in the book to avoid separation, but if things don't change significantly over a select period of time, he/she usually doesn't have a choice in fairness to all the other soldiers who are within the regulation. Generally, those on the Weight Control program also are failing the PT test, so the effect on the other soldiers is cumulative and ends up being a morale issue.
In most cases, you will get a General discharge and this will prevent you from using the Montgomery GI Bill or the Post 9/11 GI Bill. It really comes down to your commander and how he/she want to discharge you.
If there is a well documented medical reason why you are either overweight, or not able to lose weight, then your discharge may be for a medical reason. In that case, your discharge would most likely be honorable and you would retain your GI bill benefits.