since the carry permit lets me carry a weapon, is it illegal for it to print when under your shirt? If people can open carry, why would showing a little outline of the weapon once in awhile be a problem?
A permit allows the permitholder to legally carry a concealed _handgun_, not just any kind of weapon. It does not, for example, give legal cover for carrying one's concealed Bill Bagwell Hell's Belle bowie knife.
However, while the permit is officially a "Concealed Handgun Permit," it also means that local firearms ordinances are preempted for the permitholder. There is no state law ban on the open carrying of firearms with the exception of some powers granted to the Nebraska Game & Parks Commission. Local ordinances regulating the open carry of firearms are preempted for permitholders. This means that there is no legal prohibition on the open carry of firearms that are otherwise legally in one's possession, while one is in a place where he has a right to be, and absent some other facts that tend to suggest a criminal threat or other crime (e.g., you shout profanity, say "I am going to get you!," and pull up your shirt to show your firearm; or you are in possession of illegal drugs).