Guess you joined the wrong service. HYT (High Year Tenure) is determined by each service themselves. In the case of the Army, yes, HYT is at 20 years for an E6, but in the Navy, HYT isn't until 22 years, and waivers can be requested to exceed it.
As far as the overweight thing? Personally, I think it was a good thing, since in the Navy it can actually impact a ship's readiness to fight. I personally knew of 2 Chiefs who were too overweight to fit through a scuttle hatch on my first sea tour (the small round one in the middle of the large one that was closed for battle drills), and when GQ was called, they had to wait for them to get through before the main hatch was dogged down, as they couldn't fit through the scuttle.