[DTV]

I'm sure Weekend 24 continued for a bit after the Breakfast launch - although it was just a name with standard BBC News 24 branding at that point.

Yes, the Weekend 24 brand was used off-screen until the 2006 relaunch. In the earliest days of Breakfast, the Saturday edition was officially just one hour on News 24, with 'Weekend 24' following for two hours (and at least simulcast in part on BBC Two), though presented by the same presenters and only namechecked as Weekend 24, with no special branding. 

In 2002, Two's Saturday morning news block was extended and the whole thing was listed as 'Weekend 24', though still including Breakfast branding in part. By around 2004, it settled into a three-hour Breakfast block, followed by one hour of News 24 listed as 'Weekend 24' - with ISTR Bill Turnbull presenting the whole four hours, but with Carrie Gracie? taking over at 09:00.