It's called Bond paper - not available in stores as far as I know.
It usually comes in big industrial sized rolls, but you can also get ink test pads. Best place to look would be an industrial supply company like BYK or similar.
However.... (and this is a kicker) it's designed for Nitrocellulose, Polyamide or Polyurethane solvent based inks with highy rheology. Your average water base inkjet will just not print onto bond paper.
As CDan suggests, use a glossy paper.
IMO the best heavy card would be a Cornwall stock - that's the kind of stock that good quality corporate brochures would be printed on. Again, I'm not sure where you could get this in a store, but it's heavier than a bond paper.