Interesting. I never would have thought to put copper on the floor. My countertop copper is 16-gauge. I wouldn't consider anything thinner than that and would probably go thicker. Will this be near and entry door? If so, realize that any time anyone walks in with wet shoes, those footprints will show. You will also want a metal break or other method to bend the edges over so that you won't have any sharp edges at the seams.

Thanks for the thoughts, Alice. We're not sure on the whole thickness thing. We are wondering how important thickness is vs doing the sub floor properly. We were thinking we would treat/coat the floor with something for the water tracks and spills but don't know too much about that either. I have googled a little bit but I havent found anything like it.

Looks like copper flashing.

It is normally 16 oz/sq. ft. and and therefore about 0.016 inches thick.