Do any nutrient, vitamin or mineral speed up metabolism enough to help weight loss?
The answer to this is, in a word, no. There are no supplements or anything like that that have been clinically proven to increase metabolism to any great extent.
A person's metabolism can be increased to some extent by gaining muscle mass. Muscles need more calories per pound than fat does, so the more muscle you have, the higher your metabolism will be. But there are no artificial ways to boost your metabolism. There are a lot of pills and such that claim to do this, but they are not regulated and do not have to prove their claims.
Here is a line from the Mayo Clinic's site:
Don't look to dietary supplements for help in burning calories or weight loss. Products that claim to speed up your metabolism are often more hype than help, and some may cause undesirable or even dangerous side effects. Dietary supplement manufacturers aren't required by the Food and Drug Administration to prove that their products are safe or effective, so view these products with caution and skepticism and always let your doctors know about any supplements you take.