Both camps have a real argument, which is why the habit survives contact with other people. Over puts the loose end away from the wall, so you are less likely to brush the wall or cabinet with your knuckles, the end is easier to see and grab, and the manufacturer's pattern (and the folded point hotels make) faces outward. Under hides the loose end for a tidier look and, more practically, makes it much harder for a toddler or a cat to unspool the whole roll by batting at it; it also unrolls less in a moving caravan or RV. The over side likes to cite Seth Wheeler's 1891 perforated-roll patents, whose illustrations mostly show the paper coming over the top, although at least one shows it under. Surveys repeatedly put over near 70%, and the minority position is held strongly rather than casually: in a Kimberly-Clark survey of 1,000 Americans, about a quarter said a wrongly hung roll annoyed them and roughly 30% admitted to flipping one in someone else's house.