You absolutely are gaining weight from your IUD--that was my first side-effect too. Others will almost certainly follow. Get it out. I don't care what you spent: get it out. Your doctor may not (probably not) believe you. The soda comment is a very bad sign, in my opinion. Bring in the side-effects list from the mirena website and highlight the ones you have experienced.
Are you breastfeeding? If so, your baby is getting a nice dose of this poison too.