Re: Assignment unlock from BF4 campaign not unlocking.

It sounds like you are asking about weapons from the campaign that transfer to multiplayer.  There are only a few weapons that do this, the MP412 Rex, the shank (knife), machete (knife), QBZ-95-1 9Assault rifle), P-90 (PDW), and the M249 (LMG).  All other weapons found in the campaign only show up in your ingame weapons cache. 

I couldn't find your battlelog page, but if you post it I can look to see what you have unlocked, or you can speak with a game advisor at EA customer support to see what is and is not unlocked.  You can contact a game advisor here: 

1 Click on the following link: https://help.ea.com/contact-us
2 Make sure you are logged in (top right corner)
3 Click on the blue button "Contact a Game Advisor"
4 Enter the name of your game or product (or "Origin" for account-related issues) and click "Find Solutions"
5 Select the type of issue and the platform you play on, and click on "Find Solutions".
6 Click on the blue button "I still need help" if the FAQ articles do not apply to your situation.
7 Select a contact option. Note that you may get different contact options depending on your country.

I recommend that you use the telephone option and the “call me” option so you don't have to stay on hold for a long time (call back feature available to North America only).