I bought the app, but it is not installing to my watch?

Try opening the AppStore on your watch - scroll all the way to the bottom and tap on "Account" then on "Purchased" then on "My purchases" (skip this step if not enrolled in an Apple family account) and then find the app and tap on the cloud icon - the app should install then. When finished, tap on open to open up the app.

Also ensure that your Apple Watch has been updated to the latest watchOS release.