What I would do is start wit the Dev tools in your web browser and load the index and check to see what has the highest load under network. That weather extension could be the source or some other extension.
Do you see a lot of GET requests in your access logs? I mean, like layer 7 DDoS stuff? I don't think you're under a layer 7 DDoS, but if you're being scraped, etc then that could slow you down.
Or it's your host.
That's a nice theme by the way.