What popular child's toy was based on a 16th century Filipino hunter's weapon, introduced in 1929 by Donald F. Duncan?

That would be the yo-yo.

Examples of drawings in the shape of yo-yos have been found in Egyptian temples. In the 16th century Philippines, hunters would hide up in trees and use a rock tied to a long rope to throw at wild animals below them. India was the location of the next historical mention of the yo-yo. A box made that year was hand painted with a picture of a girl playing with her yo-yo. Within the next 25 years the yo-yo had appeared in Scotland, France and England. The first evidence of the yo-yo appearing in the United States was in 1866 when two men from Ohio received a patent for their 'improved bandalore.' In the Philippines people were becoming experts at both making and using the toy. In the 1920s the first Filipino yo-yo was brought to the United States by Pedro Flores. In 1928 the first yo-yo company was established in California...... Although it is believed that the first yo-yo originated in China, the first historical mention occurred in Greece, at about 500 B.C. These discs were made of wood, metal or terra cotta. The more fragile terra cotta discs may have not been used for play. Back in those days, according to Greek custom, when a child turned a certain age certain toys were offered to the gods. The terra cotta may have served this purpose. A vase painting from 450 B.C. shows a youth playing with a yo-yo.

http://www.yoyomuseum.com/museum_view.php?action=profiles&subaction=yoyo

The yo-yo.

Some claim that 16th century hunters in the Philippines had a yo-yo-like weapon consisting of large disks connected by a twine. The hunter hid in a tree and flung the disk at his prey, somewhat in the manner of slingshot, I suppose. The twine could be used to pull back the disks if his aim was off. It is also possible that the twine ensnared the animal's legs and tripped it so it could be killed more easily.

So there is some argument that the toy in the Philippines originated as a weapon, but no hard evidence. The most likely scenario is that the little round toy on a string made its way from ancient China to both Greece and the Philippines.

https://www.yo-yo.com/blog/A-Rich-History-of-a-Simple-Toy-Called-the-Yo-Yo