Many of those factors listed above help explain why a rug would curl on it's own.
However, one of the biggest reasons we come across for why area rugs curl is because they are placed on top of carpet.
As nice as an area rug might look on top of carpet, it does not come without a cost.
Because carpet is not a proper foundation under an area rug, when you step on the rug, the carpet fibers under it will compress which makes a rug move, slip, bunch up, stretch and get deformed.
Once a rug is no longer perfectly flat, it becomes a dangerous tripping hazard.