Everyone has seen NASA and other commercial entities emulate weightless flight. NASA calls is Weightless Wonder IIRC, and their air other companies that do it commercially for a price. I thought about this because I saw a bite on my locals news channel two days ago about Georgia science teachers that got a chance to experience this.
Basically, from my understanding, you climb to a pre-determined safe altitude, anywhere between 30 and 35,000ft. The they pretty much go into a series of dives with the participants not strapped in and they being to float around the cabin (correct me if I'm wrong or elaborate on the procedures).
What stresses are put on the aircraft in any? Are they any specific mods or certifications that must be done? The one I saw was done on a 727.