Do you want to follow a weather account for your town or city?
There is a Fediverse weather service called FediMeteo which has weather accounts for thousands of locations around the world:
To follow a weather account:
1. Go to https://fedimeteo.com
2. Go to the page for the town/city you want
3. Copy-paste the page's address into the search box in Mastodon etc
4. Click "Follow"
You can also follow updates about the FediMeteo project itself at @admin