Okay, I think I figured it out, but it would nice if there was a clear resource for instructions. It seems unnecessarily complicated though. Basically, you have to set up a Constant Contact Feed with an "Opt-in condition" for each checkbox you have.
So, for example, I have three checkboxes that all pertain to a separate list in Constant Contact. List A, List B, List C (obviously, each list is named differently, so that's purely for illustration purposes).
Set up a feed for each one, and capture that feed in the appropriate list. I capture first, last, and email. You have to set all of those on each feed. Then, each checkbox is captured with the custom text fields. Since I have three, I have to map each one to a different custom field. Plus, set up the Opt-in to match the Custom Field.
Here is an example:
1. Select appropriate CC List
2. Select appropriate Gravity Form
3. Map all fields you want to capture (Custom field 1 maps to List A, Custom field 2 maps to List B, etc. I didn't want to risk overwriting the custom field in CC, plus it will provide a record of it in each contact that is added under the Custom Field listing in a contact's profile)
4. Enable Opt-in Condition
5. Export to CC if untitled (leave this, mine didn't have any options) is (select your appropriate text in dropdown – all my custom text is named after each list I have to keep things simple). In this case, I'd select List A.
 You can probably skip Step 3, but it I don't think it hurts. It's up to you. This is because the Opt-in Condition ties directly to the dropdown menu which displays the checkbox options found in your form. I'm leaving mine for safety sake for now though. 
Repeat the above steps for each additional checkbox.
Good luck! Hope it works for you too.