Weapons training is not universal to Aikido - though all of Aikido has its roots connected to or even located within weapons training. Some federations practice weapons, some do not. Some dojo do, some do not. Even within those that do, as it is the same within those that don't, reasons and understandings for training with or in weapons are often quite varied (same for reasons not to train in weapons).
If I may suggest, perhaps what you saw in weapons training should not have you doubt or question weapons training itself. Perhaps such an experience is better spent having you reflect further upon what you thought or may be thinking body art is or should be or can't be, etc. Sounds more to me like a chance for horizons to be broadened - and that's a good thing in my opinion. Sounds like you are heading in that direction, so I say, "keep going." (for what it's worth)
In our dojo we practice weapons. Aside from Iaido we also do weapons training similar to what I understand you to be describing. I have some writings on our web site - which might address your request for being pointed toward more information, etc. If you have time, please check them out. There are also videos of such practice. On those video pages you will find descriptions that might also prove to be informative - granting we are just one dojo of the many that train in weapons. What you will read is our take on things, but I imagine there is some universal stuff in there as well.
Here are the links to the writings and the videos: