While scope height over the bore will effect trajectory to some degree
With a 100yrd zero, we add the same inclination in MOA as we add in inches per scope height over bore. So 2” scope height over 1.5” scope height only adds 1/2moa inclination.
Most folks don’t realize, however, that raising a scope actually gives us LONGER range access. Using a 3” scope height instead of 2.1” (what is actually on my rifle), I would have 0.2mils, .7moa, less drop compensation at 1,000 yards.
Equally, we get a longer maximum point blank range by raising our scopes. Using 3” optic height instead of 1.5” on my 30-06, a 4” MPBR extends by 20yrds. This is pretty simple - raising the sights leaves more room for rise in the early trajectory, so instead of having only 1.5” of play under a +/-2” MPBR, we can make use of more “under” before we go “over” and long before we fall back to “under” again.
Too many folks are stuck on “lowest possible scope height.” Your body is what it is - you have a specific geometry which fits between where you place a buttpad vs. where your cheek falls on the comb vs. how tall is the distance between your cheekbone and your eye. The “lowest possible” idea really stems from the amalgamation of multiple older paradigms:
1) All rifles used to have iron sights, so they all had super low combs (lots of drop) to put the shooters eye right down on top of the receiver - where the sights were located. When we added a scope to those rifles with low dropped combs, now our “sights” got an inch or more taller, but the combs didn’t move. So we needed the scope as low as possible to help keep our “cheek weld” as kind of still a cheek weld, or at least a jaw weld, and not a floating face… what SHOULD have happened, instead, is those shooters should have changed their stock fit to function properly with their body and their optics. There’s really no reason a manufacturer should have ever left an iron sight compatible stock on any model which did not come with iron sights. But they didn’t change, and shooters got stuck with poorly designed stocks for optic integration, and believed “lower is better,” instead of realizing their comb should have came up when their sights came up…
2) Hunters like small, handy firearms. Tall firearms are bigger than short firearms, and apparently every millimeter is absolutely critical to many hunters. Guys talk about hating “big telescopes” on hunting rifles all of the time, Leupold even came out with their ridiculous “L series” with a cutout in the bottom of the objective bell and lens to let 50mm objectives be mounted as low as 40’s… 10mm extra height is less than a half inch… this was silly from its outset, but it’s popular… so hunters wanted scopes really down low to their rifles.
3) Shooting super small targets without accurate range measurements at short ranges, we do see tighter convergence of low sights to the bullet trajectory. This falls apart really quickly, and we really have to be comparing extreme differences for it to matter at all. Comparing 1.5” scope height to 2.5” scope height on my 30-06, the lower scope is within a 1” target at 28yrds, whereas the taller scope is within the target at 50yrds, only 22yrds difference on the front end, and within the target at 50yrds, but the taller scope hangs onto the 1” target for 20 yards extra at the back end… for the 0-200yrd bunny hunter, the taller scope would be the advantage…
So functionally, there really is no advantage to a lower scope.
There’s also a pretty extreme advantage to a higher comb and a correspondingly higher scope, bringing the shooter’s face more naturally upright - no more “Weatherby eyebrow”. Our neck is in a more comfortable position, and our forehead isn’t pressing towards the objective bell.
I drank the “low scope koolaid” for a long time and I also for a long time passed that advice on to others myself, but any objective comparison for higher vs. lower almost unilaterally favors higher scopes over lower.
Here’s a fun demonstration, for those interested: