Mail.app doesn't load new emails because is synchronizing a deleted email with large attachment
First disconnect from the internet AND quit Mail.app.

Second, click on the Finder icon in the Dock. Choose the 'Go' menu in the menubar and hold down the 'option' key on your keyboard. With the 'option' key held down, you'll see an item in the menu called 'Library' - this is your user library, and not your hard disk or system library.

From this Library folder, you'll see the Mail folder. Navigate through V2/{yourEmailaddress.mbox)> and hunt around for either /Recovered Mail/ or /Drafts/ folders inside. It's in there somewhere. Delete the file or the entire folder if there's nothing else inside that you want.

Once that's done, reconnect to the internet, but do not start Mail. Go to your webmail provider and ensure that the file you found above is not on the server. I know you said you checked that already, but you should check again that there is no 'recovered mail' or you're going to have to start this whole process all over again...

Once that's done, restart Mail and reconnect to the internet. 

From the menubar at the top choose Mailbox > Rebuild.