BB's own towels are rentals; they are smallish bath-size. I'm afraid I don't remember the charge.
We bring our own beach towels, and they are NOT Disney towels.
Everyone and his brother buy Disney towels while they are there, and they all look sort of alike, so it becomes hard to detect which chairs are yours. (Also, I've more than once overheard people complaining to park security about stolen Disney-themed towels, often purchased new that day at the water park, but of course, not labeled.) Ours were purchased at a discount store near home; they are neon bright and visible for quite some distance. DS also takes them to summer camp, so I identify our towels with our last name painted along the selvage in fabric paint. We just pack them flat under the flap of the big suitcase.