That's the thing, I'm pretty sure you're not supposed to remember the weapons.
I personally don't get the fuss over videogame weapons, it's never been something I've grown attached to in any game, unless it's something like the Master Sword where there's a story reason behind it. But so many people will get a strong and cool-looking weapon in a game and grow so attached to it, I honestly just can't relate. And I think it's clear Breath of the Wild wasn't made for people like that.
The problem is (imo), lots of people are accustomed to play a game just for extrinsic rewards...and that's because most AAA titles have accustomed them play that way. ie. I complete the task -> reward -> I get to see the next piece of narrative; I finish the side mission -> I get a new rare item; I beat 500 enemies -> I get a trophy to display online...etc.
BOTW is a game designed to be played for intrinsic rewards -> the act of playing itself is the reward...in the specific case of BOTW in my experience, the act of discovery was the main reward for playing the game.