re: I’m also beginning to think that I should be much stricter about everyone having character sheets with weapons and other gear clearly listed or they don’t possess the stuff. What do other refs do?
It depends on the style of game. In Traveller I say yes they have to note it down or at least announce it, when they leave the ship (iirc there was an area in the ship which has a closet full of ordinary stuff). In a game of Shadowrun they have to have it all on the sheet, announce what they carry with them and if they didn’t note down a fully loaded spare clip then they don’t have one and if the clip in the weapon is empty, they have to refill the clip manually. In a game powered by the Apocalypse they have the important stuff with them and noted down. And they have other stuff if they can plausibly explain why their character might carry it (except there are rules for that as well like in The Sprawl).