This app was mentioned in 7 comments, with an average of 2.29 upvotes
The built-in Google Fit ones
I like Brilliant Weather. It pops up a nice interface when tapped:
https://play.google.com/store/apps/details?id=brilliantblueproductions.weatherwidget
As Dynalogix said, the stand up alert app now has a complication, which is great.
I've seen several complaints about failures for both of those. I'd suggest testing other 2.0 apps.
I'd grab a 2.0 cloud-enabled app and test. For example a weather complication you install while connected to wifi, then turn on bt and set it up on the watch.
Brilliant Weather has current temp, today's forecast, and tomorrow's forecast complications and can update the watch face image with a "weather appropriate" image.
(and yes I'm the developer :-)
This one supposedly has a weather background complication, although I haven't tried it, so I can't vouch for it.
https://play.google.com/store/apps/details?id=brilliantblueproductions.weatherwidget
Nope I doesn't exist here, using https://play.google.com/store/apps/details?id=brilliantblueproductions.weatherwidget for now, the dev has updated it to use some icons I made based on material icons. If this app exists I'm very curious about the icons used since the material icon repository does not currently have weather icons besides a cloud and a sun icon that were made for a different purpose.
Brilliant Weather is another nice one. Couple different setup options.