In Joomla 2.5.1(also 2.5.4) the Weblinks Plug-in can be edited to output direct urls for links. On line 85 of the file \components\com_weblinks\views\category\tmpl\default_items.php the url to be used in the link displayed on the web page is assigned to the variable $link. $link is then used in one of the case statements to build the Weblink. As it is written, $link is assigned a url which points back to the Weblinks on your site to keep track of the number of times a user clicks that particular link. Changing Weblinks to output direct urls will make it impossible to keep track of the number of times each link is clicked.

To make Weblinks output direct urls:
Edit line 85 of the file \components\com_weblinks\views\category\tmpl\default_items.php
From:
$link = $item->link;
To:
$link = $item->url;