I'm noticing a battery savings with the stock weather app on my AW3. I'm definitely holding a charge longer. I still get CARROT weather alerts via the watch even with the app not installed on the watch - which is what I only care about. So this seems to work for me. CARROT seems to be working fine on the phone - minus the rain warnings (but has only happened twice recently).
Edit: lol - now the stock weather app is reporting different weather than the stock weather app on the iPhone. Ugh. I think I'm going to give up on weather on the watch.
Edit: Went back to CARROT on watch. 8 degree difference between what watch says on complication and what the CARROT app says on phone AND watch say. ???
I feel your pain. This sounds like the sort of problem I was having with Apple Weather, Dark Sky, and BeWeather2 while on the public betas for 11.1-.3. It eventually became that Apple was accurate and consistent and Be was off, not updating, not tracking location, and different between the watch and phone.