WebGL requires cross-origin images to have proper CORS headers. This is a browser security requirement that does not apply to other mechanisms for loading images.
If you have a paid account, I would suggest contacting the OpenWeatherMap support team and ask them to enable proper CORS headers. Otherwise, you could set up a server-side reverse proxy on your server that makes it appear to the browser as if the images were loaded from your domain.
Is there anyway you can provide a code snippet of your original usage of the free service? It looks like I am only getting a single tile returned. Thanks for the help!
It ended up being a CORS error with the OWM people; I contacted them and they fixed it as of this morning.
Michael, I have been using the createOpenStreetMapImageryProvider for the OWM tiles, and it adds the {z}{x}{y} by default, so you have to put your API key in the fileExtension property.