How do you know when you should tighten the backlash nut?
I inspect the gantries for any play, every week or two depending on the usage, and make adjustments as necessary.
I grab the axis that I’m trying check at a solid point(s) with both hands and try to move it is slightly but firmly back and forth to check for play. You can feel and hear it if it’s quiet enough.
Make sure to check the whole lead screw for play from time to time as well.
As Michael’s stated, if you can feel some slack, that’s when I ever so slightly tighten the backlash screw (bolt) then check again for any movement. And when I say “ever so slightly”, I mean as little as 10 degrees of rotation.