I have mods available in my inventory, but any time I open a workbench, they do not show up for my weapons. My armor and helmet mods are available and I can modify those without any issue, but can't upgrade my weapons.

As I understand it, most weapon mods are specific to particular types of weapons.  So as an example, you might have a melee grip mod, but it only fits on a Telescoping Staff, and not on any other melee weapon.  You need to read the description of the particular mod to see what TYPE of weapon it will fit.
While I appreciate the Devs wanting to add some Verisimilitude to the game (in real life, a "grip" for a knife is going to be quite different from one that fits on an impact hammer), but it would have been easier for us players if they had use a color code, or some other "quick identify" method to understand what fits on what.

I wish that were the issue, but unfortunately the mods don't appear at all and aren't even viewable in the workbench despite having dozens in my inventory (as well as dozens of weapons). I'm in the process of uninstalling and reinstalling the game right now so hopefully that will fix it. 

An1Maver1ck, did you ever sort this out? I am having the same exact problem. It's hard to be good at combat if you can't mod anything at all, weaponwise.