When people say there's been an "𝑥 fold increase in such and such." They mean such and such is 𝑥 times as big.
If you get something that actually folds like a sheet of paper, the amount of layers doubles each time. One fold = twice as many layers. Two folds = four times as many layers...
Yeah, 'number'fold words in modern English are actually linguistic hold overs from before 'fold' was a verb that meant to bend something along a crease.
In a whole bunch of proto-English languages, fold or feald or fald or falt were all multiplicative suffixes (basically) attached to a number, which made a new word meaning to multiply by the number.
...
I'd be willing to bet this is also why the phrase 'doubled over' literally means that a person is bent, or folded at their abdomen.
You take the new meaning of fold (to bend along a crease) but replace it with the word that twofold literally means (doubled).
If you interpreted 'doubled over' as literally as OP is taking twofold, then the phrase should mean that a person was above something and then spontaneously grew a clone of themselves, or became twice as heavy or tall or something.
But you can fold the corners of a piece of paper, like dog earing the page of a book to make a quick bookmark, and unfolding that is very far from doubling the apparent, top down surface area.
There are many ways of folding things that are not the very specific 'fold in half' or bifolding that you are envisioning.
That’s only if you are folding the already folded paper. If you unfold after the first fold, then fold one of the halves in half, you’ll always end up with the number of folds plus one.
That still doesn’t match the intended meaning of the analogy though.
It's a separate meaning of fold. Fifth definition for Merriam Webster.
fold
5 of 5
suffix
1
: multiplied by (a specified number) : times —in adjectives
a sixfold increase
and adverbs
repay you tenfold
2
: having (so many) parts
threefold aspect of the problem