Below is a teaser but you need to google:
Separation is characterized as honorable and none of the conditions apply that are listed in paragraph 350202 of DODFMR Vol 7A, Chapter 35
Member is separated involuntarily through either the denial of reenlistment or the denial of continuation on active duty or full time National Guard duty
The member must be separated involuntarily by the Military Service concerned through either the denial of reelistment or the denial of continuation on active duty or full-time National Guard duty under one of the following specific conditions:
The member is not fully qualified for retention and is denied reenlistment or continuation under any of the following conditions:
(8) Weight control failure.
"The member must have entered into a written agreement with the Military Service concerned to serve in the Ready Reserve of a Reserve Component of the Armed Forces for a minimum period of 3 years following the separation from active duty.
a). A member who enters into this written agreement and who is qualified for service in the Ready Reserve will, upon separation from active duty, be enlisted or appointed, as appropriate, as a Reserve member by the Military Service concerned. If the person has a service obligation under 10 U.S.C. 651 or any other law that is not completed at the time of separation from active duty, then the 3-year obligation begins on the day after the day on which the member completes the prior obligation.
b). A member who enters into this written agreement and who is not qualified for enlistment or appointment in the Ready Reserves need not be enlisted or appointed by the Military Service concerned to be considered to have met this condition of eligibility for separation pay."
Member is authorized Half Separation Pay