The plugin only works with Ajax. When I went to the page, the OWM Weather snippet came up. Please see https://imgur.com/o257FVc to confirm.
Do you have any settings in your browser that could be preventing it from coming up?
I tested this in Chrome and edge, and cleared my cache and it doesn’t load if for some reason, a full-page load refreshes where it spins in the tab it works, but when you click on certain pages only the middle section of the page loads without causing the refresh, that’s when the plugin doesn’t load.
It seems that you may have turned off the display of the loading spinner in your weather setup (Edit Weather -> Layout -> Display Loading Spinner). Please turn it back on. The spinner also functions as a refresh button to execute the Ajax call again. Enabling this feature may help to display the weather information.
I turned the spinner back on and cleared my cache and the spinner just sits and spins.
I noticed that if you click on the spinner that the weather then loads, but people are not going to know to click on the spinner as it is just going to just sit there.
I take that back, it will not load even clicking on the spinner, it just sits there spinning after you change the pages.
It’s worth noting that the spinner doubles as a refresh button, although it’s not a standard procedure to use it. However, it’s a great debugging tool. If the spinner doesn’t show the weather info, it usually provides some kind of error message.
In your case, there must be something on your website that is not playing nicely with OWM Weather. I have not seen this behavior before.
I do not see any error messages displayed, I tried some other settings, and it just doesn’t load with ajax enabled.