Earlier this week I was on a 757 flight from SFO to JFK and the right engine was bouncing under the fairing under mild turbulence, and really moving 2+ cm under moderate turbulence. Is that in any way normal or cause for concern? Here's a video of the bounce with very mild turbulence. To see the bounce, zoom into the seam where the nacelle meets the fairing: https://drive.google.com/file/d/1QpegQ0FOUhJrp8vqMrshtCdBQDyJTWO0/view
Yes, it's normal. You will see engines bounce, yaw and shake, sometimes with apparently alarming ferocity, and you might wonder whether something is going to shake itself apart.
However, the fact is that the engines bounce because they can. Their mountings - which are extremely strong - are absorbing a lot of movement and energy safely. For example, they have to be able to handle the immense thrust that the engine puts out for the whole flight.
Another thing that you need to bear in mind is that many visible parts are themselves more flexibly attached to hidden and more stiffly mounted ones that are attached to each other. So you're not just seeing movement of structural parts, but that, plus the movement of the lighter, flexible coverings.
In short, there is nothing there to worry about, though it can be unsettling to see.