If a plane is painted, all the paint would, as far as I know, weigh the same amount. Hence the white IranAir livery would not weigh more than the Wunula Dreaming livery.
If it is not painted (eg American Airlines - cheapskates), the weight is reduced, but the polishing effort increased. Oh, and the planes look UGLY.
When BD changed their livery, there were pictures of the plane (B737-500) before and after the paint was applied here on Airliners.net. Have a look at them. They scrap off all the old paint and put on something new.
PS: The Pokemon scheme is a disgrace. How can anyone paint these horrible little annoyances on planes? What's next? Sailormoon scheme? Smurf scheme? Republican Scheme? George W Bush scheme? All-annoying-things-in-the-world-combined scheme? Urgh.