No. That is a normal weight. It is worth one cent. Melt value is more like two cents. Why would you weigh a penny? I see this commonly on eBay, but don't be fooled. Those "high dollar" common cents are trying to be sold by people who know nothing about collecting coins or their value. They aren't worth even 10% of the shipping cost of a forever stamp. If you don't have a Redbook for US coins, I can't recommend it enough. It is worth every cent to buy one.
Mary, while it is supposed to weigh 3.11 grams over time it can lose a tiny bit of weight in circulation. There is a lower tolerance limit and an upper tolerance limit, but even then, you want it to be as light or as heavy as possible. Standard weight 3.11 grams tolerance +/- .13 grams acceptable range 2.98-3.24. Now that being said, even if you found one that was 2.97 or 3.25 while it might be worth keeping in a flip with a notation of the weight, they will only be worth money if they are drastically light or heavy. 2.6, 2.7, 3.4, 3.5 etc.