I solved it!
Somehow gmail is overwriting the email address that I have specified in the “From Email Address” field in the eStore settings menu with the gmail address. So I changed the parser in aWeber to my gmail address and all is flowing smoothly now and the correct email is added to my AR list.
Thanks!
PS I am using the “Configure SMTP Settings” plugin from http://coffee2code.com/ to manage the WordPress mailer.