I move probably more than I should, at least that is what I think. Sure, movement can be extreme, but for me I think it is somewhat equal to effective camouflage while hunting whitetail - you can shoot them in jeans and a white t-shirt if the conditions are right. You have to set the conditions for your success.
I transition from leaning to sitting, I slowly sway from side to side as I scan the area I am hunting, and I adjust my tether length when needed. I actually like to move around up there in a tree because it is fun and would probably stop hunting altogether if I stopped being fun.
? Do deer see me and move on without my realization? Probably
? Do I often see deer without them seeing me? Absolutely; verified true
? Have I had deer actually walk closer to my tree to get a better look at me? Yup, once that I was aware of and she didn't spook after taking a peek.
I personally think that movement is predicated on your set up. If set up with enough effective cover you can get away with lots of movement. If hunting a tall tree where the nearest branch is 30' above your head you cannot get away with as much movement. Hunting close to a bedding area or a on a food source?
Some considerations for me include: prevailing wind and anticipated wind direction, location of deer and anticipated approach of deer, optimal shot set up, cover restrictions (bow limb interference), hot food sources, etc.
To me it seems that I usually pick the wrong tree, oriented with my back facing the actual wind direction, sitting on an old and expended food source, in an area void of deer. To counter this inevitability, I frantically SWING from side to side to find that one lone traveler looking for arrows...and I can't wait to get back out there!
...and then there are those dadgum squirrels to contend with. I move more because of squirrels than any other reason, yeah, it's the squirrels.