It seems to me that soda is basically sugar water, with the only bad thing being excess sugar consumption, which isn't a problem unique to soda.
Actually, soda can contain aspartame, HFCS (high-fructose corn syrup), phosphoric acid, caffeine, and/or empty calories, all of which are a lot more dangerous than generic sugar water.
Most of the problems seem to be related to weight gain and as this doesn't seem to effect me I wonder if I have any reason to cut it out of my diet.
Weight gain is only one of the many negative results from soda consumption. Sodas can increase insulin levels causing obesity, high blood pressure, and heart disease. Additionally, if the soda contains high-fructose corn syrup (HFCS) it is not processed in the same way traditional sugar is processed because HFCS affects (or rather bypasses) the reptin receptors in your brain which regulate satiety. Other negative effects include depleted calcium making bones weaker, hyperactivity, and caffeine dependence.
As I start to exercise, will my consumption of soda hold me back? If so, why?
The phosphoric acid in sodas leech calcium from your body and thus weaken your bones. Having weakened bones substantially increases your risk of injury as your level of exercise scales in intensity.
Caffeinated sodas act as a diuretic, which in conjunction with exercise can cause dehydration.
Finally, sodas are empty calories (calories with no nutritional value), which is generally something you want to stay away from to maintain a healthy lifestyle.
There are numerous studies confirming everything I've said which can be found in the American Journal of Clinical Nutrition, and here are two articles from LiveStrong.com which go into more detail about everything I've covered (and more).