Re: How the Unlocks Work ??

Hey Snake,

Have you ever logged into Battlelog? (I set a temp password and did so for you, which made your PSN ID show up as one of your soldiers). It also shows you now have access to Premium and Close Quarters. 

Here's a copy of a stats page. I'm not seeing 5 and 28 kills. 
I'm thinking you mean the 5 for the amount of kills. The number below it is the amount of time this weapon was used in-game.
For unlocks, you can just click the blue name of the weapon which will show the following screen:

 As you can see from the weapon screen, your next unlock will be the Reflex (RDS) scope for the SG553 in 5 kills. 
Finally, if you scroll down your stats page for the SG553 just a bit more, you'll see all the unlocks for this particular weapon. According to the list, you must have 80 kills with the SG553 to unlock the Heavy Barrel.

 

Hope this helps!