To get all your previous buyer emails, you can go into Seller Admin > View/Download Transaction, set the date range for as long as possible/desired, optionally select a specific product if you want to separate buyer emails by product, then click View Log, then click Download Log to save that log view to a file on your computer. If you're getting separate log views by product, you can select the next product, click View Log, then Download Log, and repeat this for your other products.
Once you unzip the downloaded log file(s), you can open them in any spreadsheet program such as Excel or (free) Gnumeric, select the Buyer Email column, copy that and paste into a text file or into Aweber's import screen (I'm honestly not familiar with the details of how their import function works, since they're not us :^).