The sleep issue certainly leads to the obesity. As the study indicates, but also the military schedule encourages quick food choices and energy drink use. Which is epidemic. I knew plenty of people that were good for a dozen red bull in a day. Work all day, wake up at 0300 for a watch, work all day, workout, maybe put on a fireman suit and run around a bit, four hours sleep wake up for watch, repeat. In between you eat what you can.
Sleep is an afterthought unless you are aircrew. It has been tried to implement crew rest standards into aviation maintenance, so far the best we have is rigid policies on how long before work you must be alcohol free. Now with random breathalyzer! Oh yeah, night shift, be here at 0900 for awards quarters.