Well I think 3 things could possibly be told from an accurate weight of the coin.
1. it will weigh 5.67g which would be normal - but if the coin was plated, then weight was added, and if it was exposed to an acidic environment, the coins mass would be reduced - thus bringing it back to a normal weight. Which in effect would tell us nothing really.
or
2. it will weigh heavy, indicating the coin was plated
or
3. it will weigh light, indicating that the coins mass was reduced by an acidic environment.