Here's the list of the Back 2 Karkand weapons that you can unlock.  They may need to be unlocked in a particular order and then again maybe not...

FAMAS:
10 Revives
10 Heals

HK53:
10 Repairs
1 Kill with Repair Tool

QBB-95
20 Kill with Light MG
2 Mortar Kills

QBU-88
20 Kills with Sniper
6 Lasermarker

PP-19
ARM 10 mcoms
get 10 Flags
play 2 hours karkand


second row:

L85A2:
100 Kills with assualt rifle
20 Kills with Grenadelauncher
Win 5 Rounds of squad deathmatch

QBZ-95B:
50 Kills with AT rocket
Destroy one enemy vehicle with repair tool (lol)
Win 5 Rounds of Conquest

MG36:
100 Kills with Light MG
50 Surpression Assists
50 Ammo Packs Assist

L96:
50 Headshots
50 Spot Assists
5 Kills with Knife

MK3A1
10 Kills with pp19
6 Kills with DPV Jeep
10 Kills with BTR90 Tank
Play 2 Hours on Sharqi
Play 2 Hours on Golf of Oman

You can now officially change your Origin name.  

ORIGIN NAME CHANGE

Thanks to Ares for discovering this!