There are plenty of good weather apps out there, many of which support Apple Watch, but Carrot Weather may be our favorite. It combines excellent weather forecasting (with data from Weather Underground or Dark Sky), lots of customization, a funky Augmented Reality mode, and even achievements. The snarky evil robot voice helps make weather fun.
Apple Watch support is especially robust, with several different complications available and the ability to customize them in the app. Carrot Weather was one of the first third-party apps to make use of the new corner complications on Apple Watch Series 4, and it gives you a card on the Siri watch face, too.
The only downside is that the app costs $4.99, and then for certain features you have subscribe to a Premium Club membership for $0.49 a month or $3.99 a year. The cost is to cover the increased API usage of its data sources for features like precipitation warnings.