Finish the mission(s) with these following sniper rifles to bring them into other missions.
In order to unlock a weapon, you need to start a level that has that weapon in it, find that weapon, and finish the level with it. Simulations such as the level 0 are an exception; you don't get to keep the weapons, because they are not real
The following list is most unlockable weapons, the type of weapon, and the amount of carrying capacity that it takes up. In the second column is the mission that the weapon first appears in.
The viblade is in the room with all the laser tripwires, on a stand in the center
The M60 can be taken from a guard when you fail to get let in by the front gate guard
Oh, and sniper take up 3 inventory spaces, making them unwieldy, but the jackal and shockwave can be found in rooftops escape, and bridge assault respectively.