Sifu Amin Wu teaches a number of weapons and related forms but, since joining her school, I've focused only on the chuan (empty hand) forms. Recently she suggested that I consider some weapons training so I told her about my previous experiences and that I didn't understand the point of it.
She explained that weapons training is a step towards partner training on the Tai Chi path. When you train the chuan forms you are, of course, training the hand forms for applications but they're difficult to refine without feedback from a partner. Weapons training provides an intermediate step because you have to grasp and move the weapon around in ways that harmonize the body's movements with the weapon's momentum, which provides the feedback you need to understand and improve the hand forms.
She went on to say that, traditionally, you start with shorter weapons (e.g. the Tai Chi Dao) and work your way up through longer ones (e.g. the Tai Chi Jian, Tai Chi Staff, and Tai Chi Spear), which requires better and better control. She also mentioned that many schools these days don't teach the staff or spear because it's difficult to find the necessary space.
Sifu Wu finally noted that weapons training will improve your chuan forms but you need to have a solid foundation before taking it on. When I learned weapons previously, I wasn't ready - I still had a lot to learn/refine with the chuan forms - I knew that at the time but tried them anyway because I was impatient/eager and, in retrospect, this cost me time.
I'm not sure when I'll take up weapons training again - I need to have the right class available - but, when I do, I'll know that I'm ready.