Vanilla Weapons in Fallout 4 damage are pretty underwhelming damage wise. Which makes Bethesda buffing these weapons to be slightly powerful and in some weapons, significantly strong in Fallout 76 to be a good idea.
However, those weapons buff did not transfer into Fallout 4...... until now.

Update 1.1=Now Including melee weapons, explosives and decreased weapon weight for some weapon in this list
Update 1.2=The damage buff now properly buffs energy weapon in the list.
Update 1.21=Fixed an slight typo (Uncommented slashes) that makes Flamer not getting any buff. Credit to LOLMAN6541 to point this out.
Update 1.3=Added Molotov Cocktail,Fragmentation Mine,Cryo Mine,Pulse Mine,Chinese Officer Sword,Combat Knife,Pipe Wrench,Rolling Pin,Tire Iron,Deathclaw Gauntlet and Knuckles.Pipe Bolt-Action,Pipe Revolver,Gauss Rifle,Hunting Rifle,Combat Shotgun,Double-Barrel Shotgun,Institute Laser,Gatling Laser,Grognak's Axe,Machete,Shishkebab,Switchblade,Baseball Bat,Baton,Board,Lead Pipe,Pool Cue,Sledgehammer,Super Sledge,Walking Cane,Boxing Glove and Power Fist.


With Robco Patcher, this weapon buff is ESP-less. So you can still use Creation Club Weapon Skins and Free Nexusmods Weapon Skins together.

But there is more, I also carries those weapon buff into the companion weapon counterpart and vertibird minigun too.

(Ranged Weapons)
///Combat Shotgun
/Damage 50 ---> 60

///Double Barrel Shotgun
//Cait and Hancock Double Barrel Shotgun are also affected.
/Damage 45 --> 80 --> (Update 1.3) 90
/Weight 9.0 ---> 6.0

///Flamer
/Damage 12 --> 29
/Weight 16.1 ---> 15.0

///Gauss Rifle
/Damage 110 --> 125 --> (Update 1.3) 126
/Weight 15.7 ---> 8.0

///Hunting Rifle
//Deacon and Macready Hunting included.
/Damage 37 --> 40 --> (Update 1.3) 48
/Weight 9.6 ---> 6.0

///Institute Laser
//(Not in F76,but I including this because I can't stand this weapon sucks more than their pre-war counterpart Laser Rifle)
/Damage 15 --> 24
/Weight 3.9 --> 3.0

///Minigun
//Vertibird minigun included.
/Damage 8 --> 20
/Weight 27.4 ---> 18.0

///Submachine Gun
//Silver Submachine Gun included.
/Damage 10 --> 18
/Weight 12.7 ---> 7.0

///Pipe Revolver
//Nick Valentine Pipe Revolver included.
/Damage 24 --> 27 --> (Update 1.3) 34
/Weight 4.2 ---> 3.0

///Pipe Bolt-Action
/Damage 34 --> 40 --> (Update 1.3) 45
/Weight 3.2 ---> 3.0

///Cryolator
/Damage 20 --> 24
/Weight 13.2 ---> 10.0

///Radium Rifle
/Damage 27 --> 33
/Weight 11.1 ---> 7.0

///Lever Action Rifle
//Longfellow Lever Action Rifle included.
/Damage 35 --> 65
/Weight 9.0 ---> 6.0

(New weapons in 1.1 update)
///Alien Blaster
//Hub Alien Blaster included
/Weight 2.5 ---> 2.0

///.44 Pistol
//Nuka World Bladed variant included
/Weight 4.2 ---> 4.0

///10mm pistol
//Piper 10mm pistol included
/Weight 3.5 ---> 3.0

///Assault Rifle
/Weight 11.7 ---> 8.0

///Combat Rifle
/Weight 11.1 ---> 7.0

///Fat Man
/Weight 30.7 ---> 20.0

///Gatling Laser
/Damage 14 --> (Update 1.3) 18
/Weight 19.3 ---> 18.0

///Laser Gun
//Curie, Danse and Ingram Laser Gun included
/Weight 3.9 ---> 3.0

///Missile Launcher
/Weight 21.0 ---> 20.0

///Plasma Gun
/Weight 3.9 ---> 3.0

///Pipe Syringer
/Weight 6.2 ---> 4.0

///Railway Rifle
/Weight 14.4 ---> 9.0

///Broadsider
/Weight 27.4 ---> 16.0

///Tesla Rifle
/Damage 32 --> (Update 1.3) 66
/Weight 8.1 ---> 8.0

///Harpoon Gun
/Weight 16.3 ---> 16.0

///Handmade Rifle
//Gage Handmade Rifle included
/Weight 12.8 ---> 8.0

(Melee Weapons)
///Pole Hook
/Damage 30 ---> 43 --> (Update 1.3) 50

///Assaultron Blade
/Damage 17 ---> 28 --> (Update 1.3) 38
/Weight  3.0 ---> 1.0

///Baton
/Damage 11 ---> 15 --> (Update 1.3) 26

///Lead Pipe
/Damage 11 ---> 14 --> (Update 1.3) 23

///Machete
/Damage 14 ---> 15 --> (Update 1.3) 25

///Shishkebab
/Damage 13 ---> 22 --> (Update 1.3) 29-Physical 22-Energy

///Switchblade
/Damage 8 ---> 14 --> (Update 1.3) 21

///Walking Cane
/Damage 10 ---> 17 --> (Update 1.3) 25

///Baseball Bat
/Damage 16 ---> 28 --> (Update 1.3) 36

///Board
/Damage 14 ---> 25 --> (Update 1.3) 34

///Grognak's Axe
/Damage 25 ---> 65 --> (Update 1.3) 80

///Pool Cue
/Damage 13 ---> 21 --> (Update 1.3) 30

///Sledgehammer
//Strong Sledgehammer included
/Damage 23 ---> 43 --> (Update 1.3) 50

///Super Sledge
/Damage 40 ---> 65 --> (Update 1.3) 80

///Revolutionary Sword
/Damage  16 ---> 37

///Boxing Glove
/Damage 9 ---> 13 --> (Update 1.3) 22

///Power Fist
/Damage 20 ---> 48 --> (Update 1.3) 54

///Chinese Officer Sword
/Damage 16 --> (Update 1.3) 22

///Combat Knife
/Hancock Combat Knife Included
/Damage 9 --> (Update 1.3) 21

///Pipe Wrench
/Damage 13 --> (Update 1.3) 18

///Rolling Pin
/Damage 11 --> (Update 1.3) 17

///Tire Iron
/Damage 12 --> (Update 1.3) 18

///Deathclaw Gauntlet
/Damage 25 --> (Update 1.3) 52

///Knuckles
/Damage 10 --> (Update 1.3) 24

(Explosives)
///Baseball Grenade
/Damage ---> 175

///Plasma Grenade
/Damage 150 ---> 200-Both Physical and Energy

///Pulse Grenade
/Damage 150 ---> 175-Both Physical and Energy

///Molotov Cocktail
/Now included a little bit of energy damage
/Damage 0 --> (Update 1.3) 8

///Fragmentation Mine
/Damage 101 --> (Update 1.3) 150

///Cryo Mine
/Damage 101 --> (Update 1.3) 175

///Pulse Mine
/Damage 150 --> (Update 1.3) 175-Both Physical and Energy

If you are interested to know more about the damage difference (or in general) between Fallout 4 and Fallout 76 weapons, you can look up in these websites:
(Fallout 4 weapons)
https://fallout.wiki/wiki/Fallout_4_Weapons
(Fallout 76 weapons)
https://fallout.wiki/wiki/Fallout_76_Weapons


Credits given to:
Zzyxzz for Robco Patcher
Bethesda for Fallout 4 and Fallout 76