I have a similar problem. Here is a partial solution I found on my Apple Watch 2 (without cellular).
- Open the Aero Weather app on your phone
- on the Stations page there should be a group labeled Apple Watch in addition to Nearby, etc.
- Open the Apple Watch group
- click the + sign at the bottom and find a station you want to display. Click save.
- uninstall and reinstall the watch app by using the Apple Watch app on your phone
- open the app on the watch; wait a few minutes.
This has gotten me to a display of the station list I created in the Apple Watch group. After a few minutes they updated once with data. However they fail to update from this point on. For some reason the data is not pushing from the phone to the watch. I found I could manually refresh once by going back to the Apple Watch stations list and make a change ... e.g. add another station, change the display order, etc. and then save. This seemed to force a data push to the watch. Not helpful though.
I am researching further with support at the app developer. Apple support brushed me off.