You position the background image, everything but the
fields and the button, floating on top of the CSS. You can
even fix it as part of the header or in a sidebar.

The autoresponder form needs to have every visual component
except the fields and button stripped out. Then these elements
are floated with CSS on top of the graphic.

I don't use Aweber so I cannot tell you how to modify the
code. Probably the easiest thing to do is find a site using
Aweber with a form similar to the one you want and reverse-engineer
what that site is doing.

I checked your site and it seem its already integrated with your aweber code..