Can I change "delete" to "archive" in the message control bezel in Mail.app? The version of Mail.app that comes with Mavericks has this cool message control bezel (below, in the orange box) under the email header in every message allowing you to delete, reply, reply-all, or forward the message when you hover on the line: 



It's great, but I archive all my mail. Can I change the trash can button (pink arrow) to the archive box, like in my toolbar?
As stated by CMW, Delete2Archive can solve this issue:
http://akgungor.com/2013/11/11/delete2archive-archive-gmail-messages-using-delete-key-os-x-mavericks-mail/

I use it an can confirm that it works, also for your problem:


When I hit delete on the keyboard it is archived (i.e. it stays in Gmails "All Mail")
When I hit the button from your screenshot, this seems to apply as well (to my surprise). So therefore your issue should be solved as well :)
When I hit the delete button in the toolbar of Mail.app, it gets actually deleted to the trash. You can customize the toolbar to include an "Archive" button as well (right click on the toolbar and choose 'customize toolbar'), see screenshot. I put it left from the delete button: