I'll add my 2¢, I'm not an expert, but I do have years of experience with clay bodies, kilns, firing, glaze formulations. I'm edumicated!
It looks from the pics to be a very coarse clay body that's unvitrified. This could be from under firing, or unrefined clay. The rural kilns of the 1800's were notoriously uneven firing, and far from a science. A groundhog kiln is almost a hole in a bank, not a whole lot more.
Potters of the day didn't go get clay from a supplier, but instead located a good clay deposit that fired well and located their pottery close by. Dug clay is far from the refined clay we have today. Bits of rock, sand, and small pebbles was the norm. I'd say (educated guess) that this is fairly old.
As for the thickness. In today's world we strive for thinness of our pots, but this was seen as poorly thrown back in the day. Thick meant durable. Poor clay is almost impossible to throw thinly. Remember, potters were NOT artists. Pottery was NOT art, it was the styrofoam of the 1800's. Use it, toss it. Pots were tools. Potters got paid by the amount they made, not by the amount of clay they saved by throwing thin.
This shard could be from almost anything. A churn, a jug, a bowl, a chicken waterer... Anything!
This concludes my "nerd out" moment.