The copper IUD will not affect weight gain or your moods. Since there aren't any hormones, your body behaves the way that it normally would without hormones.
Personally, I found that I am horribly moody and PMSy without hormonal birth control to regulate my cycle and my moods. Since I was bfing when I got it, I didn't have af until I'd had the IUD for 3 months and I was fine-totally loved it. But when my menstrual cycle returned, I became a ######y pms queen. Yick. Now I'm on the pill AND have the IUD.