I want to put oversized balls in a ballnut to decrease backlash. It now has standard .125 balls. I know it is probably a trial and error method, but any suggestions what size I should try first. I would rather not buy several sizes. What about opinions on alternating larger and smaller balls? I would like to hear from someone who has done this.
Thanks.

http://www.precisionballs.com/Ball_Screw_Repair.html

that is a helpful website

Perhaps you can estimate the clearance that you have in the current nut. Mount the ballscrew in some sort of a rigid fixture (like a lathe chuck, wrapping the screw with brass or aluminum shimstock to protect it from the jaws). With the balls in the nut, use a dial indicator to ascertain the axial play and the radial play. Obviously, the nut is going to ramp up and over at the same time as the balls crowd together at each limit of travel.

If you can estimate the rise/run clearances, then you can determine the clearance vector with the Pythgorean theorem.

If I'm thinking about this correctly, I think you'd estimate the change in ball size as about 1/4 of this clearance vector length, because not only are you reducing the axial clearance in either direction by an increase in diameter of a single ball, but you are also decreasing the radial clearance by 4 times, since you are dealing with balls on opposite sides of the same groove, plus the balls on the opposite side of the screw.