Please rename the “Recoil” characteristic for weapons as “Muzzle rise”
There’s a lot of discussion here about recoil values for various weapons, but of course there is NO RECOIL in the game - recoil is the movement backwards against the bullet moving forwards, and yo don’t get that unless you have haptic feedback to a shoulder stock you are using!! 
What the game does have is MUZZLE RISE - this is also due to the physics of the bullet moving one way the same as recoil, but is a different reaction - the moment (distance) between the forces acting in 2 directions gives an impulse for the weapon to rotate - a torque reaction.
the wiki article is a pretty good introduction - Muzzle rise - Wikipedia
The physical arrangement of the weapon can have a major impact on muzzle rise - a heavier weight at the muzzle end of the weapon, gas deflectors, position of the fore-hand grip for example.
so one of the reasons why the M1 Carbine has as much (or even a little more!) muzzle rise than the M1 Garand is that it is light at the muzzle end, and the forehand grip is closer to the shoulder so resists it less.
Such considerations are also why pistols can have considerable muzzle rise with relatively weak ammunition- they have little mass moment at the muzzle, and no fore-hand grip at all.
It’s not all about the weight either, guns with dropped stocks will naturally experience more muzzle rise under recoil when compared to guns with in-line stocks.
There’s a lot of factors that go into recoil intensity and direction.
Overall weight is also important, a heavier gun will be able to “absorb” more recoil energy and make the recoil feel lighter to the shooter. This is why lighter bolt-action rifles recoil more sharply than heavier self loading rifles, even when they both fire the same cartridge.
Center of weight is also an important factor for muzzle rise, as you said. The closer the center of weight is to the muzzle of the gun, the less the muzzle will tend to climb under recoil.
It gets even more complicated than that as well, even the mechanical aspects of self loading firearms. The velocity of the bolt stopping against the back of the receiver of some guns can also have a significant effect, as well as certain muzzle devices, like muzzle brakes.
In the case of the M1 Carbine though, I have fired both the Carbine and the Garand, and to me, the muzzle climb of the Carbine is definitely noticeably less than that of the Garand. Even with the significantly less weight of the Carbine, .30 Carbine is also significantly less powerful than .30-06, making for a gun that is definitely easier to shoot than the Garand.
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And my OP isn’t quite right - it is only the “vertical recoil” parameter that is muzzle rise.
the “horizontal recoil” parameter seems to be what most people think of as recoil - the shove back into the shoulder - in Enlisted it seems to be just the back sight getting a bit bigger on the screen as it get closer to the TPV eye!!
This should probably be termed “Felt recoil” or something similar to remove all the angst people have about the M1 carbine!!