This question is for more advanced martial artists...

After beginning traditional weapons studies, did you notice any improvements in your empty-hand techniques?

Oldcoach

Yes. But I would not say it enhances movements only. For instance, if you practice with sticks and learn to defend from a stick, you would find defending from a hand or a leg noticeably easier, because a stick approaches it's target much more quick than a hand or a leg does. For other instance, knife teaches you not to rely on your eyes, your view, but instead to "feel" your opponent, once you manage to touch his armed hand. That way you learn to get information about your opponents next step just by being in contact with him.

Kresho

I noticed the same kind of increase in reflexes after I started weapons training that I noticed after I started empty hand training. It is an exponential leap.

Thanks for reminding me,
OldCoach

Working with a weight during exercise often builds more muscle, than exercising without a weight, since it is more difficult.

When you build more muscle strength, you can more easily move.

If you can more easily move, you may even be able to more easily move faster.

If you can more easily move faster, then perhaps you could move even faster than that when not dragging that extra weight around.

Length of a stick, added to length of arm where it is attached, causes a increase in length (over just arm length) from fulcrum to point of application of force (end of object where makes contact), as well as a increase in "moment arm" while practicing with long object, forces more energy expenditure in order to move with more "moment arm", and more momentum.
Building muscle because of stress.

When you stop using long object it gives a smaller "moment arm" (when not using long object to practice, i.e. back to unarmed combat), and smaller "moment arms" allows more effective torque for same torque applied.

Hope that helps.

I also have some additional info under the following posts:
How to increase the speed
Martial arts and physics?