Metal Gear Solid 3 / 4 - Snake already carries a lot in just a few weapons slots (RPGs, assault rifles) but if you count the pause screen, he can carry dozens and dozens more - he just has to “equip” them for the moment. In 3, he also carries numerous spare camoflauge uniforms and all kinds of other items.
I’m going to go with the original Goldeneye, especially with the all guns cheat.
Carry every weapon in the game. Including a tank turret. Not to mention doubles of most of them for dual wielding. Plus carrying extras of the PPK and Mp5k with suppressors on them rather than detaching the suppressors.
EDIT: Just did a quick count of all the weapons in the game. Including a second for weapons that can dual wield, there are a total of 52 weapons in the game, all of which can be carried at once. 53 if you count the plastic explosives in the Silo level.
I’d say Fallout, you could carry hundreds of weapons at once if you didn’t have any other items on you.