When I consider this question, I ask what does "weight" add to the game?
So, if I were making a survival game, like Oregon Trail (that's what it is, really), I'd definitely use Weight, because limited supplies is a core concept of the game. Or, if you have a Zombie Apocalypse game, it's quite fair to make a core part of gameplay "Do you want to carry that rusty sword, or that can of lighter fluid?" Because survival games are supposed to be challenging from scarce resources.
But, if you have a classic fantasy RPG, unless it is a core part of the gameplay, what does it do?
I think the most crucial time for item limits is already there --- combat. Out of combat, I could guzzle 999 Heal potions if I want. In combat, each round I guzzle a Heal potion is a round I'm NOT beating up the enemies/casting spells/whatever.
If I want to limit the amount of money the player gets, so they can't get infinite money from, say, killing 1000 guards and selling their swords, I have several alternate ways (that could be used together) to solve this:
1. Add a virtual economy --- the more of something I sell, the less it's worth. And, conversely, the more of something I buy, the more expensive it becomes.
2. Make shopkeepers have limited amounts of cash (which does replenish over time). After all, that scruffy old man selling Antidotes in the desert probably doesn't have 300,000 Gold to buy your Awesome Sword of Death.
3. Make shopkeepers only purchase items related to what they are selling. So if you get those Eyes of Newt drops, you need to find some Alchemists who will buy them.
4. Make some of the item drops worthless for straight selling but useful for trading. I'd reserve this for only a few items, because it would quickly become VERY annoying.
Those are "realistic" without really being too frustrating for the player. Some of these even open up new RPG side quests ("Where is a vendor who will buy the Sword of Infinite Blackness?")
So I prefer more creative approaches to solving the infinite money problem. As for "limiting what the player can bring into battle", I don't see that as a problem for the reason I mentioned.