this is due to exponential growth; the increase in previous thickness is doubled each time you fold the piece of paper again. physically you could probably only fold a piece of paper about 7 - 8 times on your own.
Given a paper large enough—and enough energy—you can fold it as many times as you want. If you fold it 103 times, the thickness of your paper will be larger than the observable Universe; 93 billion light-years distance.
How can a 0.0039-inch-thick paper get to be as thick as the Universe?
The answer is simple: Exponential growth. The average paper thickness in 1/10th of a millimeter (0.0039 inches.) If you perfectly fold the paper in half, you will double its thickness.
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.
Keep folding it. 42 folds will get you to the Moon. With 51 you will burn in the Sun.
Now fast forward to 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.
90 folds will make your paper 130.8 million light-years across, bigger than the Virgo Supercluster, estimated at 110 million light-years. The Virgo Supercluster contains the Local Galactic Group—with Andromeda and our own Milky Way—and about 100 other galaxy groups.
And finally, at 103 folds, you will get outside of the observable Universe, which is estimated at 93 billion light-years in diameters.