This is awesome!
So as someone who use to work on COD weapons, I'm not an animator but the weapon designers help the animations with a lot of the screen tilts, shakes, and usually handle most of the recoil.
I highly recommend referencing the newest Modern Warfare, they had a decent amount of time and put a ton of work into their Animations.
It looks like your shake may be a little strong, but you pointed that out in one of the other comments. In my opinion, and again I was a weapons designer not an animator, I would only apply that shake when there is a force that gets noticeably distributed through the body. I think there is a shake occurring when the weapon is taken off of the shoulder to start the reload/inspect, it's awkward because it's hard to visualize that action in first-person and how it impacts the player.(You can tell the weapon comes to a stop against the shoulder when you push it back in after the reload, you can't tell when the weapon leaves contact of the shoulder when pulling away)
I would also be willing to move the camera a bit with the way the gun tilts. They use this on some weapons, but in general tilt the camera in the direction you are applying force on the gun. So when you pull the mag down and to the left slightly tilt your vision down and to the left until you push the mag back in up and to the right and reset the vision. I think there are a lot of fun ways to experiment how the camera can shift with the reload and inspect.
I also use to keep nerf guns around so that I could experiement with how things would look/feel. It can be fun to strap a gopro to your chest and go out and reload a replica or mess around with a nerf gun.
I just saw this and wanted to say good job and it instantly brought me back to working on COD weapons. Keep up the good work, I loved how you have the clamp around the barrel!(also again I'm not an animator so take my feedback with a grain of salt :P)