If anyone played older versions of the fantastic Neverwinter Nights mod Tortured Hearts, that used originally have weighted gold so you'd have to buy gemstones with your gold that weighed very little and then sell those when you wanted to buy things. This was a neat idea but it was a nightmare to deal with, I like elements of reality in my fantasy games but at the same time I also like convenience and do not want to have to spend extra time walking around to sell or buy any equipment.
There are reasons to have weighted gold and not to have it. If this is an RPG where you'll go around collecting loot and stuff then I think weighted gold would not be a good idea as it will only cause frustration. If however the game intends to be quite realistic so a character can only carry something like one or two spare weapons and a small number of potions then weighted gold is fine. I think volume is more of a concern than weight, using Neverwinter Nights as an example again, you had so much space there that even if you didn't have a high strength you could still carry loads of light armour and weapons as well as magic bags that could hold even more armour and stuff yet characters didn't require pack-mules. It wasn't realistic but it was convenient for selling things.
I think the only way you can cater for everyone is if you have options like the way you have violence options in games; hardcore players can switch on weighted gold, moderate players have the choice based on their preference and time available I guess.