How to Add "Weight" to First Person Camera?

I would like to add “Weight” to the first person camera. What I mean by that is, instead of the camera snapping to the position of which you moved your mouse to almost instantly, I would like for it to transition there in a Sine movement sort of way.

I’ve searched all over Dev Forum and YouTube but I’ve yet to find something that matches what I’m looking for. And since I know little to nothing about how this stuff works, I’ve come crying to the forums for help.

Is there any sort of things I can read up on that might help me with this? Thanks!