There is a desktop bar that contains all the widgets in your collection, which is what is showing in your screenshot. You need to open the widgets from there, to display it on the desktop like I have them. Then you can close that toolbar so that it stays in the tray as just an icon. The open widgets will remain on the desktop, unless you close the whole widgets application or the individual widgets.
Attached to this post you will find my fixed weather widget. Keep a backup of the zip file, after extracting it, in case you should need it in the future. Then just click the extracted widget to open it.
Unless you have changed the widget engine's default settings, it will ask if you want to move it to your collection. The answer is yes, move it, overwrite the original existing widget, whatever it wants. Once the non-working widget has been replaced with this one, you should be good to go.
One note about this. I only replaced an old dead yahoo.com URL in the original widget code with one from weather.com that works. The weather widget will occasionally crash if/when it receives bad feed data from weather.com, which is something I have not fixed (and do not plan to).
I am not sure which clock you are referring to, since there are 2 on my screen.
The analog clock is the Carmino Vector clock, a stand alone application (not a Yahoo widget) from here: http://www.crossgl.com/vcl_clocks.htm
The digital clock is my own DClock project (also not a Yahoo Widget), which you can find here: http://appsapps.info/dclock2.php
As far as RAM is concerned, I can't really say. It couldn't be all that much for just the weather widget, though, since I have used the whole collection you see in my screenshot, plus a ton more stuff, on an older Pentium 4 PC with 1GB of RAM. (the Yahoo Widgets engine and all widgets were written for XP era computers, which were typically single core and usually 2GB of RAM, or less)