The stock used in the current edition is fine. Perhaps you have an older edition? When did you buy it and did you buy it new or used? There was an older edition that had stock that was way too thick. But the current edition has a good quality stock; it's just not linen finish. The cards will bend if you shuffle them carelessly, but most cards will. I sleeved my copy with DragonShields. I "mash" shuffle, which is easy to do and quite easy on the cards. I doubt you are going to see future print runs with different card stock, so my recommendation is that if it concerns you, just sleeve the cards.
I bought it new about a year ago. It's the same card stock Iello used for Innovation. Works fine for those cards, but Innovation cards don't really get shuffled like the Biblios deck. The cards are so creased, I'm about ready to have to buy a new copy and that is why I asked the question about a reprint. I really don't like card sleeves.