By feel I can identify 20 lb, 24 lb, 28 lb, 65 lb cover, 110 lb cover, and 12 pt matte paper. I'm increasingly impressed by people's business cards as a result, as it is often much, much heavier than 12 pt matte.

Using comparison I can distinguish 80 lb semi-gloss cover, 100 lb semi-gloss cover, 8 pt gloss, 10 pt gloss, and 12 pt gloss. (But then again, most people could, given multiple choices rather than a free-response question.)