Did Ueshiba feel weapon work was a part of aikido, or did he not? Or did he just not want to train his non uchideschi students in weapon work (was he worried that someone he didn't know or trust would be learning it?).
I have read that Saito Sensei was the only person ALLOWED to teach weapons by O Sensei, apart from his good self.
I have heard (and it may be completely incorrect) that in Japan you go to one place to learn your (non-weapon) aikido and another to learn your weapons. (Perhaps this only happens in some places?)
I'd imagine he was just fairly particular about teaching weapons. Perhaps he was concerned that a student taught badly or not enough in Aikiken or Aikijo would be badly shown up by kendoka, Iaidoka, Jodoka etc. and acquire a bad reputation for his O Senseis Budo?