I said 'simple as that' because that is the only reason why it is 'flip floping'. None of the other stuff.
Nothing like your mouse/rat trap analogy
Thinner limbs obviously have less material in them, most importantly less wood. Wood being by far the stiffest material in a composite. The wood gives the bow its shape and is generally the cause when a bow doesn't bend right or resists bending correctly.
Horn bows made with no core are very prone to this problem.
Light weight hornbows have to have thin component pieces however I like to go as thin as possible with the horn,2mm max with the sinew and leave the wooden core as thick as possible.
Trust me a 100# bow is a whole different animal than a 40#'er performancewise and ease of tillering.
Think about making a wooden kids bow. using 'normal' adult lengths/widths etc - say 66", 1 3/4" wide but instead of 50# only 20# how would that bow react to 'normal' belly tillering (compared to a normal adults bow). Sensitive eh? The wooden bow and the hornbows have little to be able to directly compare but this shows that IF you don't scale everything it WILL NOT act the same. Your hornbow isn't a scaled version of an original and couldn't be so you have to deal with these 'issues' which arise because of the differences.