YouTube give you the code to insert in a web page.
If you want to add videos every week, you could certainly use a new blog post each time, or just insert the new code in your existing web page; which will make the page longer each week so eventually it may become too long and slow to download. If the YouTube videos all start automatically you will have to insert code to stop this, like:-
<param name="controller" value="true"/>
<param name="autostart" value="false"/>
inside the object and embed tags; but the above code may only work with mp4 files; for flash file you may have to do some research to stop autostart.
See http://stephenjungels.com/jungels.net/articles/flash-video-howto.html which may help.
If you want to change the video every week I think you will end up doing it manually but all you need to change is the YouTube file url, not the whole object tag code.