Coca-cola contains a lot of calories but very few nutrients, foods like that are called "empty calories". There is harm to the body due to regularly consuming empty calories alone. If the ratio of useful nutrients per consumed calorie goes down then that means that you would have to consume more calories to get the same amount of nutrients, which is then likely to cause weight gain. Even at the same calorie intake you may experience weight gain due to getting in less nutrients that the body needs for metabolism. The body also needs anti-oxidants to get rid of free radicals produced in metabolic processes and you'll get less of these per consumed calorie.
So, the best way to think about the harm is to consider that the fundamental source of the harm is not coca cola but it's due to simply being alive. A living organism is a very complex machine that needs to repair itself constantly. To do this, it needs to have a steady supply of many different raw materials. If you feed it a lot of fuel without these raw materials then simply cranking up the metabolism to match the fuel consumption to the fuel intake would do a lot of damage. What happens instead is that a fraction of the extra fuel is stored instead of burned while the metabolism is cranked up a bit. This limits the damage, the storage would allow the extra fuel to be burned safely if you would eat more vitamins and minerals later. However, if this is a chronic situation, then you'll end up burning energy in a dirtier way on the long term.
If instead of drinking coke you eat a large amounts of walnuts every day containing a large amounts of calories, much more than the coke you drink, then you'll hardly gain weight and your health will improve a lot.