An observation - I don't know if this is significant: Previously you stated:
Weatherlink is installed with default file locations. (C:/Weatherlink)
On the two systems that I have WeatherLink installed on (one Windows XP and one W7 Ultimate), it's installed at C:\Program Files\WeatherLink
Weatherlink is started, either at boot from StartUp directory, or from desktop icon if it had been closed.
I presume that, after startup, you shut down WeatherLink? And then occasionally "start Weatherlink 6.0.3 with a desktop icon"? That is, you aren't running two copies at the same time?
Just for safety, please go confirm that the two "icons" have exactly the same properties, etc. e.g., right-click on the desktop icon and select "Properties", write down that information, and compare with what it says in the startup.
I am the Admin, and the only one using this computer.
Unless your account name is "Administrator", that's not what I meant when I said try running WeatherLink as Administrator.
Right-click on the desktop icon, and select "Run as Administrator".
Also, what is the status of the .wlk files? (in particular, date/time of last update, etc.