"a King who was so fat, that he had his fat sucked out by leeches."

An illustration from the Histoires prodigieuses les plus mémorables qui ayent esté observées, depuis la Nativité de Iesus Christ, iusques à nostre siècle: Extraites de plusieurs fameux autheurs, Grecz, & Latins, sacrez & profane, by Pierre Boaistuau, known as Pierre Launay, published in Paris in 1560.

This image and others from the book are stored at the Wellcome Collection website. I'm familiar with the use of leeches for phlebotomy and to remove excessive edema fluid or hematomas in plastic surgery patients, but I doubt they could have extracted fat.

Found at the Monster Brains blog.