I got an email last week about this, and now your weather tweets will no longer be forwarded to your FB pages. Sucks
Facebook Connect A recent update to the Facebook Platform Policies ended the ability to automatically post Tweets to your Facebook profile or page.
This finished for me about 8 months ago, if you do not use the weather pc as a main pc then you could setup a macro, i use one to open a custom file and collect the data i want to post to fb, copies it, closes the file, opens a browser that has my weather page as the home page using the mobile* version of fb, it pastes it and then posts it, then closes it, very simple but highly effective.
Look up Mini Mouse Macro, its free, but if you want the macro to close when its finished you need to pay for the pro, or you can set up a batch file to close it 