I can now tell you what the issue is and what needs to be done, but I can't tell you in detail how to do it, although I think I could figure out how if I was going to do it but I decided not to, at least for now. The issue is that CumulusMX does not process and upload the graphs like Cumulus 1 did. Instead, the (blank) graph images get uploaded to your site only once, manually by you, when you first install CumulusMX, and CumulusMX only uploads and updates the data for the graphs, and the data gets added to the blank graph images in the browser, using javascript, when you or anyone views the page (client side processing rather than server side). So the only way to get it to work is to somehow incorporate the graphs page that comes with CumulusMX into your Weather By You template. Or perhaps somehow modify your WBY template to work the way the CumulusMX one does using javascript. I reverted back to Cumulus 1 for that reason and because it has some features I prefer. Anyway that's the issue. I had a PM conversation with Steve about it on the Cumulus forum and he explained it to me.
Also - I made a mistake in my post above yours - the graphs are Cumulus graphs NOT Weatherlink. It had been so long that I forgot where they came from.