Anthonie was the son of Gijsbert Duyck, lord of Oud Karspel, who was appointed schout of Hoorn in 1580.
As official of the Raad van State, he accompanied Prince Maurice of Orange on his military campaigns between 1591 and 1602.
Oldenbarnevelt was an important political leader, while Duyck was more an official, and held this office for eight years, but without putting his stamp on it.
Anthonie married twice, and his first wife, Elisabeth de Michely, gave him three children, all daughters.
From 1591 to 1602, Anthonie kept a journal, detailing his activities and events of the Eighty Years' War, in which the Dutch Republic was embroiled at that time.