The normal weight should be 2.70 grams. It could be just a bit more or less just like all other coins.
Because the 1943 steel cent was a true oddity, thousands were kept and many in AU to MS condition. While I've seen prices on these vary from 5¢ to $1.30 for common condition, they are only worth what someone is willing to pay. Take this information from someone that has well over 500 of them, inherited from my grandfather.