Really, an across-the-board PE requirement wouldn't be a bad thing. I'll go so far as to say it's a requirement every semester you attend--including the summer sessions. I know, not everyone's into team sports or aerobics. Offer a full slate. Offer self-designed independent study. Just set standards for it and hold the students accountable. Play a varsity sport, and you want to count your off-season conditioning? Fine, but your attendance has to be documented. We used to play rollerblade tag on the quad most evenings. Document the nights and the locations--provide a means to be checked up on. I played pickup hockey with friends, I can count that too, just have the rink staff sign when I arrive and leave. Whatever you do, don't cut people slack. Don't let them stand around. If they can't run, they walk--but they do it longer, so it's actually worth something.
"I didn't come to Lincoln to be told that my weight is not in an acceptable range." You probably didn't come to Lincoln for a lot of things. That's nice you're a three-time honor student. Your body mass isn't "slightly high". It ain't healthy. You knew the policy when you came in. You chose to stay at your private university. Lay off the Cheetos and get your ass in the pool.