Gold should weigh... SOMETHING but not enough to burden you completely.
and enough to make money not useless.

Gold/Silver bars, Gems/crystal, or just junk items that can be only sold for money and have no other fucking purpose in game but to be sold for in game money..... SHOULD have weight.
(i HATE these type of items if they are in every chest i find and after many hours it make money useless)

money itself should be weighted but you should be freely able to carry around 1000~ thousands of gold coin with ease and item prices should depend on that.

ok, i have admit something shameful here but I CHEAT!
i always cheat money after playing ANY game after a certain time in or on my 2nd/3rd playthroughs.
i always do it.. I will likely do with same with weight if it becomes a huge problem and i don't feel like rpg-ing it up.

Also keep in mind as i said before money can become useless... because there are not enough items to buy or you so much of it, its pointless now. So having weight on money/gold can be good thing to balance it out.