You don't waive it exactly, but you must give permission in order to proceed. Your rights are still intact because you have the right to turn around and walk out without a search. This is the same as at a nightclub, for example.

The important difference is that, since you at no point waive your rights, you have the right at any point to withdraw consent for further searches, turn around, and walk out. My understanding is that taking a weapon into an airport is a crime, though, and that once you're past the checkpoint if law enforcement has probable cause they can detain and search you. I'm sure I won't find any argument, though, when I say that refusing a voluntary search does not constitute probable cause and that if anyone tries to detain you for refusing a search and turning back from the checkpoint, you should get in touch with the ACLU.