I've searched everywhere for this, but can't seem to find anyone who has the same problem.
Basically, I am carrying six or seven mods for a variety of weapons, yet when I select the weapon in my inventory and press the "mod" button (LB) the mod menu is empty.
YES I have checked that the weapon is moddable and YES I have checked the mod is the correct one for that weapon. NO I am not using a unique weapon.
It doesn't matter what weapon I select in my inventory, the 'mod' screen is always BLANK no matter how many mods I'm actually carrying. This is SO frustrating! I have some cool ones but can't use any of them. Is this skill dependent? My repair skill is up to about 70.

try putting some of the mods onto a follower, then modding a wep with one you still have in your inventory...or try putting them all onto a follower, then bringing them back over to you. not sure what happened, but i would try several different things to try and 'reload' the mods into your inventory.

It might be the infamous "Repeat item" glitch.

Are you carrying more than one of the same mod? Go to a safe place w/ no people around (Novac motel room, for example) and drop all your mods on the ground. Pick up one and try to mod again.

I've had this glitch happen with 'Recruit Helmets' and '10mm pistols.'

Essentially, the item is still in your inventory but it either duplicates itself OVER an existing item of the same name or becomes unuseable altogether.

I noticed my weight was going up but I wasn't carrying anything more than I had been. It was because I actually had 5 recruit helmets (when only 1 was shown) in my inventory and didn't know it. When I sold the one I could see, the 4 hidden ones magically re-appeared.

I had that happen with a BB gun. I had one in a chest and one in my inventory. Whenever I tried to put the one in the chest into my inventory it would only show that I had one BB gun. But it would act like two if I put one down. I just went and sold one so I wouldn't have to worry about it.
The major duplicate problem seems to be with throwing spears. When I first came across throwing spears I thought they had a certain number of 'throws' in them or something. I just drop those now.. It's too confusing to try to keep track of how many I have and selling them barely works. I'll be able to sell a few but then when I look in my inventory I'll have seemingly more than what I sold.. and I've never stolen any.

Thanks for your replies!
Last night after a lot of stuffing around, it suddenly started working! It somehow fixed by doing a combination of the things you suggested, so thanks everyone