As a Pilates instructor, my job was always to help people move more symmetrically so this fit tip is a little counterintuitive to me, but I love it anyway.
Once a month, deconstruct your weight routine and work one side of your body at a time. Instead of doing your standing bicep curls or overhead presses simultaneously, split them up. Work the right arm for 10 reps and then the left side for the same; doing so will make your core work to keep you balanced since you're working asymmetrically. Do single-leg squats, too, and hold only one hand weight when performing lunges. Be sure to switch hands halfway through your reps though — you only want to push the asymmetry concept so far. Working unilaterally will also help improve your coordination. Plus, it is always wise to shake up your routine every once in a while to keep your gym experience fresh.