Be aware that adjusting bearings is a delicate job. Obviously you want to tighten the bearings a bit, but be careful, since you can brinnel (mash) the bearing surfaces if you apply too much force. The standard advice (that I know of) is to loosen the outer lock ring and then screw in the pivot pin gently until it makes contact (wiggle the arm a bit to see that the pin is seated). Back of an eighth of a turn, and then tighten the lock screw without tightening the pivot screw - a bit of a problem sometimes,
You need a bit of slop in bearings because nothing is infinitely perfect - ball bearings and ball races have slight variations and if you tighten up enough to eliminate slop, the bearings will quite possibly bind.
Also - and very important - make sure the slop you are trying to eliminate is actually that of the vertical bearings, not that of the horizontal pillar bearings. This is a bit overstated, but essentially correct) the horizontal bearings rely on gravity to keep them tight - the upper race is the one that matters, and the lower race is just there to keep the upper race ball bearings from falling out - and gravity keeps the mass of the arm tight on that upper race. So if you torque the arm checking for loose bearings, if you find slop, make sure it is not the entire arm in the pillar bearings. The slop of the whole arm in the pillar is integral to the low friction of the arm - you want the arm rolling along the top race, with no dragging from the bottom race.
So check by pressing down gently at the pivot point of the arm, and see if the slop is in the vertical bearings before you do any surgery. It may not be necessary.