As Marissa said, if it isn't specified for the swap the only "expectation" is that your cardstock be acid-free. Personally I don't care about my CS being really heavy (card weight) because it just adds to the thickness & weight of the page. I figure once it goes down on the page no one will be playing with it.
Either Mikes or JoAnns (can't remember which, sorry) carries loose cardstock by Die Cuts with a View. It's usually included in their sales - 5 or 6 for $1. This has a "woven" texture to it also, just not as pronounced as Bazzill. (That's part of the appeal of Bazzill for me...the texture.)