Some weapons unlock by upgrading others to the MAX, you'll then need EXCHANGE POINTS (EP) to buy them under Bonus Features - You get EP from completing missions or Mercs missions, a better rank/difficulty nets you more EP You get 2000 for an S rank 1500 for A rank etc. Other weapons can be found in cases scattered around the levels.
VZ61 - in mission 1 in a case in the corner after the executioner smashes the gate open. It'll be on your right hand side far corner.
Shotgun - in mission 2 you get a key which can be used in the area with the Cephalo
sub-mg at the start of mission 3 in the garage
S75 Rifle in a case in the room near exit with heli support.
SVD Rifle - in locker when encountering gun emplacement.
S&W Magnum - in chapter 3 after you've unlocked the door that required the pieces, you'll see a dead BSAA member and the magnum at his feet. You'll get ambushed here.
M3 Shotgun - when opening the second gate 3-3 head to the shack by the waters edge.
Rocket launcher purchasable after 3-3 or found on the destroyed ship in the lake in chapter 3-3.
Grenade launcher - in case at bottom of stairs after then track and field QTE it's opposite green statue on its left.
Ak47 in monitor room during chapter 5-1
sig 556 at end of conveyor belt.
PSG1 in room with switch during chapter 5-3
Jailbreaker at base of large stairs
L.Hawk - purchasable from store after 5-3 or found in tomb during boss fight in Chapter 5-3 (after getting kicked through door by boss).
Sig pistol in store after 4-4
Longbow - upgrade S75 rifle to max.
Hydra - upgrade any M37 shotgun to max - costs 30,000