Webmail uses IMAP, where mail is stored on the server. IMAP uses several subfolders under each folder for storing messages (cur, new, tmp). I'm guessing it has something to do with IMAP making a copy or moving a message. POP3 then sees it as two different messages...
The easy way to fix it would be to use IMAP all the time, but Outlook 97 doesn't support IMAP. You'd have to get 98+ or switch to Outlook Express.