Well come on Del, I'm waitin'
I have no idea how medieval bowyers did it, they had rope, their workshop probably was timber framed with convenient trenails protruding to hang bows on.
Maybe there is no record, because they simply didn't consider it a tool... it's just a bit of rope.
I'd guess they probably didn't bother with weights, or if they did, it wasn't a calibrated weight in the modern sense. Possibly just a big stone and some marks made on a beam.
I use string when marking out a bow, but if I did an inventory of my workshop I wouldn't include string, and I won't be mentioning it in my will!
Absence of evidence isn't evidence of absence.
Making bows for the war effort could easily have been 'making bows by numbers', get 'em up to floor tiller and move 'em out for the next guy to trim 'em up and put on nocks... dunno, I don't think anyone does. I've read theories which didn't stand up to close examination, so I think it's better to confine ourselves to facts rather than conjecture.
But... if we are allowed to dream, then maybe they had buxom wenches helping them... yeah, that works for me
Can I quit and have my dinner now?
Del