Paint is heavier, but it's not significant. Wraps caught on because you can change your "look" quicker, which is an advantage in today's sponsor changes almost every race.
Mark is correct about lighter drivers having an advantage. It allows you more flexibility in bolting weight will it helps handling. NASCAR ended up changing the weighing rule to include the driver (used to be car only) because big drivers like Michael Waltrip and Jimmy Spencer were at a disadvantage. So a lighter driver isn't as much of an advantage anymore, although it still is an advantage. Makes me surprised there haven't been more women drivers, but the Good Ol' Boy network is tough to crack...