Like Gerardo, I'm a fan of koryu weapons, though by geography I'm out of that option for the foreseeable future.
Within aikido, being an aikimutt, I've done a few years of Chiba Sensei's weapons, a few years of Tohei Sensei's kata and more recently more of Saito Sensei's weapons, with a teeny bit (as in a day at a time for a total of maybe three times) of Kato Sensei's weapons.
While each has its own very distinct flavor, I find they have in common several things in terms of how they enhance empty hand technique (and here I am talking specifically about partnered practice, not solo kata) :
- increased focus because of a greater sense of potential danger ("I'm gonna hit you with a stick!")
- learning to look at the whole person, not just the weapon helps with noting small movements, weighting, etc as well as zanshin
- if you are taught, as I was, to remain outwardly impassive during weapons, you find this carries over when you want or need it to in empty hand (although I've been known to spend a lot of time smiling on the mat, training joyously :-) )
- issues like centerline, entering, claiming centerline, where your center is aimed, etc become much more obvious when the weapon is several feet longer
- so does timing, especially as in weapons we often start by taking turns doing each strike/block and then, without speeding up per se, do them in a flowing manner
- if you can enter and deal with shomen from a jo or bokken, it is a lot easier to do irimi on a shomenuchi
- for movement challenged people like me, memorizing 20 to 30 part long weapons kata makes any empty hand technique seem pretty simple in terms of "getting" the gross movements :-)