If you're right handed like me then it's almost certain that your right side is stronger than your left. Whether right or left handed, your dominant side can affect your balance and over time one side of you becomes more worn than the other. I went to the physiotherapist and she noted that the muscle behind my left scapula (that big triangular bone on your back, just below the shoulders) was less dense than the muscle on the right. She detected this because of the comparative ease with which she could massage the muscle below my left scapula.
She gave me an exercise to do in order to strengthen my left side, so that's what I'm preoccupied with at the gym these days. The funny thing is often you can't see any discernible difference between your left and right sides - they look equally developed and strong when you look in the mirror. When you do weight training, always be wary of your strong side compensating for the weaker side. This happens in exercises like the benchpress or leg press when both your arms or legs are pushing the same weight in unison. A way to counteract this is to use free weights i.e. a separate weight for each arm or leg. This ensures that your weaker side gets an equal workout. You can go one better and do some extra repetitions on your weaker side.