When clicking on a message (link), you are telling the browser to do a redirect to that link, which will result in a new page load.
Instead, you need to call $.colorbox via javascript. Change your links from:
<a id="ajax" href="message/read_message.php?messageid='.$row['message_id'].'">'.$row['message_title'].'</a>
to
<a id="ajax" onclick="showMessage($row['message_id'])">'.$row['message_title'].'</a>
In your Javascript add the following function:
function showMessage(id) {
$.colorbox({href:"message/read_message.php?messageid=" + id});
}
Hope this helps!