Weapons videos come in many forms. What I want to gather here are videos of the bokken and jo katas of Saotome sensei.
Saotome Sensei Kumitachi
The bokken kata that Saotome Sensei introduced, practiced as a standard in ASU dojos, are quite different from those introduced by Saito Sensei and more widely practiced in Aikikai dojos. There are excellent instructional DVDs available (for instance here and here), there are also some fine examples on the web. I put a few here, although there are quite a few more.
Kata 1-5, Aikido Shobukan Dojo, Washington D.C.
Robert Deppe, Rokudan, and Cliff Judge (please let me know his rank if you know him)


Kata 1-15, Budo Dojo, Portland, Oregon
Dan Penrod, Godan, and Partick Martin, Shodan
Kata 1-5, Utsusemi Aikikai, Houston Bay, Texas
Ken McGrew (please let me know the rank if you know him)
Saotome Sensei Jo Kata
I need to add the jo kata as well. You can what’s around the web by searching for Satome Jo kata