Ooh...weaponized antigrav guns...I like that thought!! If Iran screws with us, we'll just flip of their gravity and laugh while their whole country is flung into space. Too cool!
On a more serious note, of course a private citizen should own the patent. There are already laws that allow the government to circumvent patents for national security reasons, so owning a patent on an antigrav generator would be no different than owning a patent on any other kind of technology. Many of the components in our weapons and aircraft are patented by non government agencies, and this would be no different.