The oldest knife I know which looks like a balisong is dated from the end of the 18th century (179?). It's called "Pied Du Roy". I found it in a Cutlery Museum in France.
There's a photo there :
http://www.balisong.net/en/history.htm
What I know is that martial arts weapons were banned in the Philippines when they were under Spanish Rule. About 103 years ago, when the Filipino people were "liberated" from the Spanish by the American people, the ban on martial arts weapons was droped. At about that time, a man from France helped the people in the Batangas area to start up a knife making industry.
Most of people think that the balisong comes from the Philippines. That's true that the name "balisong" and the fashion came from here. But the idea of the knife, the concept of separating the handle in 2 mobile parts... some people think it comes from Europe (the Spanish would have brought it to the Philippines Islands).
Still not sure if the Balisong is a European innovation or that the Balisong was independently made by Filipinos and the whole design in Europe is possible a coincidence.