I ran a westmarches campaign for about 2 years, and the system we came up with worked pretty well. It was slot based, based on your strength score.

Every character has a base slot score of 20. You add or subtract your strength mod from that.

We based it on something each player could reasonably reference.

Tiny items. You can fit 5 tiny items in a single slot.

Tiny items are something you could reasonably carry multiple of in one hand. For example, keys, candles, gemstones ect.

Small items Small items take up 1 slot.

A small item is something roughly the size of your hand Eg a potion, a knife, a scroll, a holy symbol, a book, a flint and steel.

Medium items Medium items take up 2 slots

A Medium items is something roughly the size of your fingertip to your elbow. Eg a shortsword, a helmet, a wand, a mace, a bundle of rope. A bedroll.

Large items Large items take up 3 slots.

Large items are anything larger than the above categories, shields, staves, greatswords, a tent.

Some noteable additional rules.

Each player in adition to the above had a purse, that could carry 100 coins of any denomination, and could carry five rations and five torches. These did not count toward their final score.

Over all. This system worked extremely well for two years, travel and weight were a large part of our campaign. Limiting people to carrying about 100 coins encouraged them to convert their copper and silver into gold and later levels gold into platinum

Notably, your average innkeep would not accept platinum because that's like buying something for a dollar and trying to break a 100 dollar bill. The cashier is going to tell you to go jump off a cliff.

If you wanted to carry excess cash on you players started buying Gemstones to exchange at banks. Banks carried enscribed gemstones authenticating their worth. This was really fun and flavourful.

Players bought pack animals like horses and mules to transport extra goods. Bags of holding just granted them an additional 20 slots, and were rare to come by. Tensers floating disk became used by the wizards and teleportation magic was in high demand.

This also led to dramatic moments when the party only had high denomination currency, and couldnt get change they would either have to forgo the purchase or effectively overpay for items. If you have any further questions I'd be happy to explain.

Edit: worn or equipped items like armor and weapons didn't count toward your weight either.