Unfortunately once a contact has unsubscribed they would need to sign back up on their end. There are several ways to do this but the quickest is to send them a link to your sign up form outside of Constant Contact. They would just need to click this link and follow the directions. Here's an FAQ with some other directions if one of these works better.
As for the unsubscribe process, it's hard to be opted out from a forwarded email since the unsubscribe page requires you re-enter the original recipients email address. Thanks for your feedback on this!