For anyone thinking about playing New Vegas again, check out Viva New Vegas! Fixes the gunplay, bugs, lighting, crashes, balance, and adds new important features like expanded consequences for your actions, cut content, a post-game where you can see the consequences of your choices, and better visuals!
I've heard it's mostly due to either low strength, weapon skill or in the case of the Hunting Rifle and Survivalist's Rifle, faults in the model itself.
That's how weapon sway usually works, alongside innate weapon spread, but there are legitimately misaligned iron sights at 0 spread and perfect stats, unintentionally from the devs. Other fun bugs include increased aim shaking when further from the center of the worldspace, micro stutters, an inability to play beyond 60FPS without destroying physics, weapon lighting assuming light sources are not where they actually are, and more!
All of these are fixed, and result in a New Vegas as you remember it, not as it actually exists. Absolutely worth playing with VNV.
I wish I didn't notice them, but a lot of my play sessions end with the game hardlocked and having to kill it in task manager. Still doesn't stop me from playing it regularly tho.