What methods of birth control (other than condoms) don't have weight gain side effects? or at the least just a bit of weight gain?

IUD: While most birth control pills have been studied and found to be 'weight neutral' (so most people neither gain nor lose weight)- any hormonal contraceptive will have a chance of causing weight gain), the paragard iud is a copper intrauterine device) that has no hormones so should not cause any weight gain. Other barrier methods too (diaphragm, female condoms, etc).