It took a few google searches until I could find out how to change the default weblinks order. A lot of websites showed how to do this via the admin back-end panel in the advanced configuration... I can't see this panel, there is no advanced parameters under a weblinks category.
The issue is that suppose a menuitem links to a category of weblinks, the default sort order (as in the first time you view the page) is the order in the admin panel (not even by most recent). I'm going to show you how to do this by title in ascending order without installing any 3rd-party extension as well as by any of the database values used by each link.