I've been playing PC RPG's since the late 80's a quite a few of them did have systems in place where money had weight (like Pool of Radiance and other gold box games). Personally I think it makes sense, but I think you need the right kind of game mechanics to support it and make it fun.
For instance, in the Gold Box games there wasn't just "gold"...you had various types of money. There was copper, silver, gold, and platinum. In the main city there were banks that you could convert 100 copper to silver, 100 silver to gold, etc...so you could reduce the weight you are carrying by converting less valuable metals to less (quantity) but more valuable metals.
If money has weight we should also be given cool storage options. Not just a barrel in a house, but (like the above example) possibly a bank or vault where we could make deposits and withdrawals.
Anyways whatever you guys decide I think would be fine. While weighted money (with the appropriate supporting mechanics) would totally be cool with me, it's not a feature I think I would miss either. Just not that a big of a deal I guess :P