Can also stream it at Internet archive:

https://archive.org/details/WeatherChannelMusic

https://archive.org/details/weatherscancompletecollection

https://archive.org/details/lfset1

https://archive.org/details/the-weather-channel-presents-the...

https://archive.org/details/the-weather-channel-presents-smo...

https://archive.org/details/weatherscanlocalmusic

YouTube has a few TWC playlists:

https://www.youtube.com/playlist?list=PLMUZjd023YBtp0iB962Uz...

https://www.youtube.com/watch?v=hYyTo0ex76Q&list=PL2UoJXK3rr...

https://www.youtube.com/watch?v=wmGd-cx-dXc

It’s on Twitch:

https://m.twitch.tv/retroweatherchannel?desktop-redirect=tru...

There’s a nice Spotify playlist:

https://open.spotify.com/playlist/0WEViIh23PGbLqGbjYNAZz

And the site dedicated to it mentioned earlier in the thread has some recordings:

https://twcclassics.com/

Many for sale here: https://www.ebay.com/sch/i.html?_nkw=Weather+Channel+Music+C...