Very slightly enlarging a hole?

After doing some measuring, I wonder how tight I should be shooting for, in principle?

The test hole I made with the 0.251" reamer wobbles almost imperceptibly, and varying a little depending on where on the rod it's positioned. If the rod varies from 0.2505 to 0.2508", how tight a hole is "tight" but non-binding?

I also wonder how paranoid I need to be about this. The main goal of this tight but sliding fit is to maintain as close to a right angle to the rod as I can. Of course, that right angle is also dependent on the machining of the brass piece too, i.e. is the hole actually perpendicular to the flat on the brass piece. Any error from perpendicular is multiplied by the 36" long rod length.

On my test piece, the "flat" was faced on round stock in a lathe prior to drilling and reaming the hole (in the same set-up), so it should be pretty good. The final piece, however, would be cut from a ~3" long by 7/8" wide rectangular bar, which would be more difficult to hold and face in my toy-sized (Sherline) lathe.
 
Is there a reason why you cannot attach the brass to the rod with two split collars? The collars could be made of brass and their weight could be subtracted from the main weight.
 
Or you could heat the brass by 200C. The hole will expand by 20ppm/C x 200C. This is 0.004". (For a 1" hole, or 0.001" for a 1/4" hole.) The brass is dropped on the rod, using a stop. When the brass contracts, it will lock on to the rod, if you sized the original room temperature hole correctly. If you need to move the weight, heat the brass again. Might take a couple heatings, but you should be able to position it.
 
Is there a reason why you cannot attach the brass to the rod with two split collars? The collars could be made of brass and their weight could be subtracted from the main weight.

If you have been following along with my Kater's pendulum project, this is for the non-weighted end, which needs pivots, too. The weighted end can be fixed (e.g. with a shrink fit, as you describe), but the other end's pivots need to slide for adjustment over a reasonably wide range, in a very delicate and precise fashion (very tiny adjustments will be needed). At the moment, I'm expecting to use a set-screw to fix that position, but still with a tight fit when the screw is loose.
 
By the way, maybe I should start a project page for this instead of just asking random questions from time to time? Maybe the metrology category is a good home for that?
 
After doing some measuring, I wonder how tight I should be shooting for, in principle?

The test hole I made with the 0.251" reamer wobbles almost imperceptibly, and varying a little depending on where on the rod it's positioned. If the rod varies from 0.2505 to 0.2508", how tight a hole is "tight" but non-binding?

I also wonder how paranoid I need to be about this. The main goal of this tight but sliding fit is to maintain as close to a right angle to the rod as I can. Of course, that right angle is also dependent on the machining of the brass piece too, i.e. is the hole actually perpendicular to the flat on the brass piece. Any error from perpendicular is multiplied by the 36" long rod length.

A 36" long by 1/4" diameter steel rod supported horizontally from the ends will sag 0.050" just from its own weight. If cantilevered from only one end it will sag a half-inch. Of course, maybe you are mounting it vertically so its weight doesn't tend to bend it. Doesn't change the fact that a 36" by 1/4" rod is about as stiff as a well-cooked noodle.

What are you using this arrangement for? Does it have to be free to slide in service, or does it get positioned and then locked down? If the latter, I'd slit the block and use a screw to clamp it down. You could use the 0.251 reamer for a nice sliding fit, then lock it for zero slop.

On my test piece, the "flat" was faced on round stock in a lathe prior to drilling and reaming the hole (in the same set-up), so it should be pretty good. The final piece, however, would be cut from a ~3" long by 7/8" wide rectangular bar, which would be more difficult to hold and face in my toy-sized (Sherline) lathe.
 
How wide of an adjustment range? More than an inch? Was thinking of something like a micrometer head or a differential screw.
 
By the way, maybe I should start a project page for this instead of just asking random questions from time to time? Maybe the metrology category is a good home for that?
Not sure of the category, but you need a project thread. Random questions tend to get random answers. If the questions are in one place there's some context.
 
If you have been following along with my Kater's pendulum project, this is for the non-weighted end, which needs pivots, too. The weighted end can be fixed (e.g. with a shrink fit, as you describe), but the other end's pivots need to slide for adjustment over a reasonably wide range, in a very delicate and precise fashion (very tiny adjustments will be needed). At the moment, I'm expecting to use a set-screw to fix that position, but still with a tight fit when the screw is loose.
Set screws are the spawn of Satan!

Joking aside, a set screw will mar that nicely polished shaft, leaving a burr that will hang up in your nicely fitted brass part. If you absolutely must use a setscrew, make sure to put a flat on the shaft so the burr will be kicked up on the flat and won't touch your brass. Better would be to split the brass part and using a clamping screw, or make a split cotter or something like that.

Edited to add clarification (googling "split cotter" just finds cotter pins, not what I'm talking about). This guy is making a split cotter:
 
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