There's a note at the end of our Aweber instructions about that:
NOTE: Newly subscribed buyers will receive an opt-in email from Aweber, with a link they must click to confirm their wish to subscribe. For checkout methods that support an opt-in/-out selection the buyer must opt-in for their email to be submitted to Aweber (PayPal Website Payments Standard does not have an opt-in/-out, so those buyers will always be opted-in automatically).
I.e., for card-based Direct Payment checkouts with PayPal Pro, the buyer needs to check "Sign-up for product updates and newsletter" in order for their name/email to be submitted to Aweber, and then they must click the link in the confirmation email they receive from Aweber to approve their subscription. I've also improved the introductory wording of that help page section accordingly. Express Checkouts using a buyer's PayPal account should opt-in buyers automatically just like Website Payments Standard.
The text of that checkbox cannot be customized, as the code which generates that checkout page is shared in common among all our merchants; however, buyers probably aren't familiar with our Updates service for issuing free links, so they'll likely just interpret "product updates" as meaning news updates about the product.