Why does the 757 fuselage bend more on turbulence than those of other airplanes?
This is really two questions


Why does a fuselage bend?
Why does the 757 fuselage bend more than others


I'll give the simple answers here. You can go into a LOT of detail, but the detailed answers are mainly just bringing more information on design/engineering differences into the simple answers (eg composites bend/break in a different way to aluminium)

Why does a fuselage bend?

Essentially, it's because the lifting force doesn't support the entire fuselage equally. Drag and the aerodynamic forces created by the fuselage itself will also affect things, but it's mainly due to the fact that the lifting force is centred on two points of the fuselage, while the weight is spread along it

The lift is generated, primarily, in two places: the wings and the horizontal stabiliser (some is generated in the body too, but relatively little). Most of that lift is generated at the wings, which are attached in the middle(-ish) of the fuselage. Imagine balancing a ruler (fuselage) on your finger (wings), then stacking coins along the top of the ruler. The heavier the rule, and the more "lift" your finger has to provide, the more the ruler flexes.

Of course, lift isn't constant - turbulence means that over a few second the lift provided by the wings can change quite a lot. Imagine you start bouncing your finger up and down, creating "turbulence": the ruler will flex and unflex as it absorbs that changing force. This is the fuselage flex seen in aircraft.

The fuselage will also bend while landing or taking off, because you're again changing how the weight of the fuselage is supported: the weight is transferred from the wing root/spar to the landing gear. And the final obvious one is that the weight of the aircraft changes during the flight due to fuel burn etc.

Why does the 757 flex more than other airliners?

Well, for one thing I don't see any sources for this other than "I've heard that" (the links you provided are mostly hear-say too), but I have seen it stated as fact. Let's, for the moment, assume it's fact... the theory applies regardless.

The 757 will flex more than some other airliners (although likely less than some others) because of its design, construction and the build materials. The simplest explanation is that it's one of the longest narrow-body airliners.

What does that mean? Well, it means it's one of the longest, thinnest fuselages around. This gives us two causes:


The 757 flexes more than other large airliners because anything bigger than it is a wide-body aircraft, which will resist bending more than a small, narrow bodied thin one
It flexes more than other small airliners because any other narrow body is lighter and shorter than the 757, providing less force on the fuselage and requiring a smaller lifting force.


TL;DR: Flex is caused by lift acting mostly in the middle(ish) of the fuselage, while the weight of the fuselage and other forces on it are spread out along the length.

Overall, then, the 757 is on the boundary between lighter, narrow bodied aircraft and larger, wide bodied ones. Anything smaller than it weighs less so stresses the narrow body less. Anything larger has a bigger, stronger fuselage.