The field you can pass over API are Full Name (or First and Last Name fields) and Email. If you want to pass those to Aweber, they can be passed via API and you can learn how to do that here:
If you want to pass any other fields, for instance, custom type input forms, you will have to do that with the help of the web form.
To learn how to do that, please, follow this video:
If you have any questions or concerns, please contact our support team by emailing firstname.lastname@example.org or by clicking the support icon in the bottom right-hand corner of this page.