There’s a slight bug in Fallout 4 that causes your weapons to go invisible while you’re in first-person mode. It’s very annoying, as you’ll be unable to aim down your sights or do much in the way of aiming at all, for that matter.
To fix the issue, you’ll just need to do the following:
1) Enter third person mode (hold down the ‘back’ button if you’re using a controller)
2) Holster your weapon and unholster it (hold down the Square button on the PS4, or the X button on Xbox One)
3) Get back in first person mode.
That’ll fix it.
For further technical guides on Fallout 4, be sure to check out how to use console commands on the PC, the best settings to use to maximize your performance, how to disable mouse acceleration, how to change the FOV, and how to fix any stuttering.