AHA - so that's why...!
Once I wanted to weave with paper yarn, and to that end used one of the old wooden reeds.
After a while, I noticed that the dents were not evenly spaced:
Yesterday I came across the doubleweave portion of Zielinski's "Master weaver" where one can get several suggestions as to how to handle the fold when weaving double width.
(Methinks the first idea is the best: "experiment")
"Another method is to have special reeds made with dents growing wider towards the fold. Such reeds of rather old vintage can be found in antique shops. The difficulty here is that regardless of the width of the woven fabric the fold must be always at the edge of the reed, which may result in weaving off the center of the loom, unless the reed can be shifted in the batten at will."
I found that an adorable suggestion, which also might have explained my "variable" wooden reed...
Except it doesn't, of course. The open part wasn't even near one end, and wasn't even near to be systematic, whatever that may mean. And no, there weren't dents missing/fallen out, 'cos they usually show...