I think you are asking a great question. I am a fan of knowing the "why" behind some rule/guideline/statement.
If I think about what happens at the end of a shot at the limb tip, I realize that the string stops the motion of the limb tip. If there was no string the tip would go past its resting point and oscillate back and forth like a spring until it came to rest. So what we have is a rapid deceleration of the moving tip. Two key factors seem to be how much energy needs to be stopped, and how abruptly does it stop. The weight of the bow, the weight of the arrow, the draw length of the archer and efficiency of the limb design/string combination determine how much energy is stored at the release of the arrow. The string characteristics seem to determine how abruptly the tip stops. The characteristics of the string that seem to be important is its strength and stretch.
A 16 strand string with each strand having 25# tensile strength has a 400# tensile strength. A 16 strand string with each strand having 50# tensile strength has an 800# tensile strength. What about stretch? Let's say the 25# strands stretch 10% with a 50% load (for discussion sake). The 50# strands stretch 5% with a 50 % load. So the 16 strand 25# string will stretch 10% when subjected to a 200# load. The 16 strand 50# string will stretch 5% with a 400# load.
Using a 50# bow, for illustration purposes, let's say that all 50# is available when the tip needs to stop. The 16 strand 25# string will stretch 2.5% (50#/200# x 10%). The 16 strand 50# string will stretch 0.6% (50#/400# x 5%). This says with full strength FF strings the tip is stopped in 1/4 of the distance that the B-50 string stops the tip. Talk about slamming on the brakes!
Another aspect to consider is the area over which the stopping force is applied. If the 16 strands of FF are smaller diameter than 16 strands of B-50 then the force exerted at the point of contact with the string is also increased. Let's pretend the FF string is 1/2 the diameter of the B-50 string.
Now you have 4 times the force applied over an area 1/2 the size. This might indicate that at a minimum you need 8 times the resistance to the force. This could be in 8 times the thickness of the tip material, or 8 times stronger glue, or some combination of the two.
The actual thickness could be better estimated by knowing the real values for strength, stretch, diameter and force to be stopped.
For the same bow, same arrow and same archer the ratios hold true, so all that is really needed is the strength, stretch and diameter of the strings.
This seems to be consistent with some of the thinking on skinny FF strings with padded loops. An 8 strand 50# string now has a 400# tensile strenght with a 5% stretch at a 200# load. So the 50# bow will stretch 1.25% (50/200 x 5%). The paddled loops make the diameter at the contact area the same. Now the tip stops in 1/2 the distance (brakes aren't slammed quite as hard) and the force is applied over the same area.
The reduced stretch of the FF string probably adds to the amount of force to be stopped, unless it imparts that force to the arrow in the form of greater speed.
Just some of the thinking that goes on in my head about this subject.