I have found that each weapon can spawn more frequently from different missions. Here's a full list of weapons and the missions that will start to have a chance of that weapon dropping. In order of difficulty and stage order within each difficulty. I left easy out as they are the same drops as normal difficulty.
-----WEAPON NAME-----DIFFICULTY-----STAGE NUMBER-----
-----Assault Rifles-----
AF14-----Normal-----01
AF14-RA-----Normal-----03
AF14-ST-----Normal-----06
AF14-RAR-----Normal-----10
AF14-B3-----Normal-----12
AF15-----Normal-----16
AF15-ST-----Normal-----21
AF16-----Normal-----27
AF-V-----Normal-----29
AF16-RA-----Normal-----34
AF17-----Normal-----40
AF18-----Normal-----49
AF18-RA-----Hard-----8
AF18-X-----Hard-----10
AF19-ST-----Hard-----14
AF19-----Hard-----21
AF19-RA-----Hard-----31
AF19X-B3-----Hard-----41
AF20-----Hard-----46
AF20-ST-----Hardest-----12
AF20-RAR-----Hardest-----21
AF21-B4-----Hardest-----28
AF99-----Hardest-----34
AF99-ST-----Hardest-----39
AF100-----Inferno-----27
-----Shotguns-----
Buffalo G1----- Normal-----01
Buffalo G2-----Normal-----08
Governor 25-----Normal-----19
Wideshot-----Normal-----24
Wideshot VR-----Normal-----30
Sparrow Shot-----Normal-----32
Buffalo G3 Burst-----Normal-----37
Buffalo G3-----Normal-----42
Sparrow Shot M2-----Hard-----12
Governor 50-----Hard-----16
Wideshot A1-----Hard-----26
Buffalo G4-----Hard-----37
Wideshot A1-VR-----Hard-----43
Buffalo G9-----Hardest-----11
Sparrow Shot M3-----Hardest-----19
Governor 100-----Hardest-----37
Buffalo GSS-----Hardest-----42
Sparrow Shot MX-----Hardest-----48
Buffalo Wide-----Inferno-----37
-----Sniper Rifles-----
MMF40-----Normal-----01
MMF40-RA-----Normal-----05
Stringer-----Normal-----09
MMF41-----Normal-----13
MMF41-B3-----Normal-----19
Lysander-----Normal-----28
MMF42-----Normal-----36
MMF42-RA -----Normal-----45
MMF43-----Hard-----13
MMF43-B2-----Hard-----21
Stringer J2-----Hard-----28
MMF50-----Hard-----33
Five Card XA-----Hard-----37
Lysander 2-----Hard-----43
MMF100-----Hard-----48
Five Card XB-----Hardest-----11
MMF200-----Hardest-----27
Lysander F-----Hardest-----44
Lysander Z-----Inferno-----42
-----Rocket Launchers-----
Stingray M1-----Normal-----01
Stingray ST-----Normal-----02
Volcano 3A-----Normal-----10
Stingray ST2-----Normal-----15
Volcano 3w-Burst-----Normal-----19
Cascade 1-----Normal-----21
A1 Plasma Launcher-----Normal-----24
Goliath D1-----Normal-----36
Stingray M2-----Normal-----42
Stingray M3-----Hard-----09
A2 Plasma Launcher-----Hard-----15
Cascade 2-----Hard-----19
Goliath D2-----Hard-----25
Stingray M4-----Hard-----34
Volcano B10-----Hard-----41
Goliath Z-----Hardest-----11
Volcano 6W-----Hardest-----17
A3 Plasma Launcher-----Hardest-----23
Stingray M99-----Hardest-----32
Stingray MF-----Inferno-----30
-----Missile Launchers-----
Air Tortoise 01-----Normal-----01
ME1 Emerald-----Normal-----02
MLRA-----Normal-----04
Air Tortoise 02-----Normal-----07
ME2 Emerald-----Normal-----10
MLRA-2-----Normal-----21
ME3 Emerald-----Normal-----32
MLRA-3-----Normal-----45
Prominence M1-----Hard-----11
FORK-A20-----Hard-----15
MLRA-TW-----Hard-----25
MEX Emerald-----Hard-----40
Air Tortoise ME-----Hard-----48
Prominence M2-----Hardest-----31
FORK-X20-----Hardest-----40
Prominence MA-----Inferno-----29
-----Grenade Types-----
MG10-----Normal-----01
MG10J-----Normal-----01
UM1 Grenade Launcher-----Normal-----01
MG11-----Normal-----05
UM1-J Grenade Launcher-----Normal-----06
MG12-----Normal-----12
Stampede M1-----Normal-----12
UM2 Grenade Launcher-----Normal-----16
MG13-----Normal-----18
MG13J-----Normal-----25
UM2-J Grenade Launcher-----Normal-----27
MG14-----Normal-----30
MG14J-----Normal-----33
UMRA Grenade Launcher-----Normal-----37
UM3-J Grenade Launcher-----Normal-----41
Splash Grenade-----Normal-----47
Sticky Grenade Prototype-----Hard-----8
MG20-----Hard-----12
UM4 Grenade Launcher-----Hard-----14
BRUTE-J Triple Grenade Launcher-----Hard-----19
Splash Grenade a-----Hard-----30
MG21J-----Hard-----32
BRUTE Triple Grenade Launcher-----Hard-----39
Sticker Grenade-----Hard-----45
Stampede M2-----Hard-----46
MG29SJ-----Hardest-----15
CRUMBLE Twin Grenade Launcher-----Hardest-----15
Sticky Grenade a-----Hardest-----31
UMAX Grenade Launcher-----Hardest-----40
Stampede XM-----Hardest-----46
MG30-----Hardest-----48
-----Special Weapons-----
Burner-----Normal-----01
C24 Hand Bomb-----Normal-----06
P78 Bound Gun-----Normal-----07
Flame Thrower-----Normal-----11
Firecracker 1-----Normal-----11
ZE-GUN-----Normal-----13
Acid Shot Prototype-----Normal-----16
Y10 Impulse-----Normal-----16
P79 Bound Gun-----Normal-----23
ZER-GUN-----Normal-----26
C24 Bomb-----Normal-----35
Firecracker 2-----Normal-----39
ZE Sniper-----Normal-----41
Y10 Wide Impulse-----Normal-----43
Acid Gun-----Normal-----44
Firecracker 3-----Hard-----8
C25 Special Bomb-----Hard-----22
Flame Thrower a-----Hard-----15
Y11 Impulse-----Hard-----16
P80 Bound Gun-----Hard-----23
Acid Shot-----Hard-----30
Firecracker 4-----Hard-----39
Y11 Anti-Aircraft Impulse-----Hard-----43
ZERA-GUN-----Hard-----43
C26-----Hard-----48
Wide Acid Gun-----Hardest-----15
Burst Firecracker-----Hardest-----17
Super Acid Gun-----Hardest-----23
P89 Bound Gun-----Hardest-----25
Flame Cannon-----Hardest-----20
C70-----Hardest-----36
ZE-GUN10-----Hardest-----40
ZEX Launcher-----Hardest-----48
Y21 Impulse-----Inferno-----27
Magma Cannon-----Inferno-----30
ZEXR-GUN-----Inferno-----32
-----Bonus Weapons-----
Zero Laser Rifle-----Easy Completion
ZE Launcher-----Normal Completion
Y20 Impulse-----Hard Completion
PX50 Bound Shot-----Hardest Completion
Genocide Gun-----Inferno Completion
Full disclosure: I need only four more weapons, not including the inferno and hardest completion, Stingray mf, buffalo wide, zerx gun and magma cannon.