I was thinking about that too. The way I've heard and used it all my life is that. Threefold == 3 times.
I'm now wondering if I've just been taught wrong as is common. Fold once and it doubles the thickness, twice four times, so three folds would be eight times.
Exponential growth.
Language gets misused and abused all the time, so this difference in meaning wouldn't surprise me.
For some examples, "it's all up hill from here" I grew up with meaning things will only get better. Years ago the people in the work environment confused me with "it's all down hill from here" meaning to them that things will only get easier from now on. One day, I'll figure out the difference between button-up and button-down shirts.