B737 Captain reported the rudder was not operating properly during preflight check and subsequently refused the aircraft.

Narrative

I found the plane to have a very small change in force 3/4 through the right rudder input. It was not always felt on every push of the rudder. I looked at the back of the plane and the rudder seemed to very slightly catch on the throw to the right at about 80 to 90 percent through the rudder throw. I verified little to no wind. Mx (Maintenance) said they felt it too; but could not identify an underlying cause. I coordinated my findings with the Chief Pilot and Maintenance Control.I feel this was probably flyable; but I think that if I was standing in front of a bunch of FAA officials (in the event something happened); I would have a hard time justifying why I took an airplane that I felt was not 100%. This maybe capable of being flown by a flight test team to a repair location.In my professional opinion; the rudder issue is probably not anything big. It could be a pulley that needs lubed or some part of a PCU (Power Control Unit) that is wearing out. If I was a passenger; I would want a 100% plane which is why I chose to give it back to Mx instead of taking it.