But seriously... some time ago, I started playing around with an old webcam monitoring program that would upload via FTP, and it just wouldn't connect. I checked the FTP server URL, and it "was correct", kept banging my head, and as you did, tried a separate FTP program which worked fine.
Well, when I finally looked at the URL very carefully, letter by letter, I realized that I had reversed part of it, from "www-ftp" to "ftp-www", or something like that. Once corrected, the old program worked fine--but I was convinced for hours that I had verified the correct URL...
That wouldn't explain why the FTP URL in Weatherlink might have changed... but is there any chance your ISP changed their FTP server URL?
When you tested FTP with another program, did you let that program dial in? Or were you already connected to your ISP via dialup, then ran an FTP program?