What stops a piece of paper from being folded more than seven times?

 Nothing stops a piece of paper from being folded more than seven times if the paper is thin enough. Depending on the thickness and width of the paper, after a certain number of folds, the paper stack becomes thicker than it is wide. After that point, there simply is nothing left to fold, so the limit is reached. Each fold in half makes a paper twice as thick, so that n folds of a paper that has a thickness of t results in a total thickness of 2nt.

Every time you fold the paper, the area is halved and the thickness is doubled. The latter furthermore means that the next fold will take up twice the space, as the thickness has to "go round" the layers for them to be folded.

2 to the power of 7 is 128. Standard A4 80 g copy paper is 297 mm long and 0.1 mm thick. So after 7 folds, you would have less than 2.5 mm length and 12.8 mm thickness. Actually, you can't fold it more than 6 times this way because the thickness going round in each fold would consume too much.

To fold it 7 times, you would need to fold it alternatingly in both directions. And if you folded first 5 times in one direction, then 3 times in the other direction, the sheet can be folded 8 times. 

However, given longer or thinner paper, it can be folded more times, thus voiding the myth of the "7 times" limit. And as a mathematical problem, there is no upper limit. However, due to the power of two the practical limit is rather low. As far as I know, the record is still 13 times set by the St. Marks Students. 

FACTS ABOUT FOLDING PAPER :

Folding the paper in half a third time will get you about the thickness of a nail.

Seven folds will be about the thickness of a notebook of 128 pages.

10 folds and the paper will be about the width of a hand.

23 folds will get you to one kilometer—3,280 feet.

30 folds will get you to space. Your paper will be now 100 kilometers high.

42 folds will get you to the Moon.

51 takes you to the Sun.

81 folds and your paper will be 127,786 light-years, almost as thick as the Andromeda Galaxy, estimated at 141,000 light-years across.

Finally, at 103 folds, you will get outside of the observable Universe, which is estimated at 93 billion light-years in diameters.

So how many times you were able to fold the paper, tell me in the comment section😁.