A caveat.
I had the change to perform a similar experiment at work testing very sensitive accelerometers. Believe it or not, the biggest source of errors was the bending of the floor due to the test masses!
A better setup would be to suspend the spheres exactly like the tuna cans, and test two configurations rotated by 90 degrees.
For the accelerometers the problem was the tiny tilting of the sensitive axis in the gravity field. In this case you're probably right that this doesn't matter -
but in general it is difficult to rule out every second-order effect when the forces at play are so small with respect to g.
OK, that I guess that kinda-sorta makes sense if the accelerometers were rigidly mounted to the floor. Was that the case? Because if so then what you would have would basically be a seismometer, and floor bending from the test masses would, it seems to me, be the least of your worries.
Yes, the accelerometers were mounted on an optical bench and of course we could detect any minor earthquake (sensitivity was around 1e-10 ms^-2).
The bending of the floor due to the presence of people in the room was noticeble indeed.
I assume if your weights are resting on the floor, and the pivot point of the swing arm is resting on the floor, then the floor deflecting may cause the arm to swing even in the absence of an attraction to the weights.
That's true, but the details of the placement of the ladder doesn't matter at all. The only thing that matters is that the ladder doesn't move or wobble around during the experiment.
