Somehow I tapped a link in the default Samsung AccuWeather weather widget and switched it from always going to the AccuWeather website to the Weather Channel app. How do I get it back to always going to the AccuWeather website?
Install the AccuWeather app. The Weather Channel app goes to the Weather Channel site, you can't make it go to the AccuWeather site. (From what you say, though, you should have the AccuWeather app already installed. Delete the Weather Channel app and drag the AccuWeather widget to the home screen.)