In the 13th century soldiers began to strengthen their protective mail. They used metal plates to protect the places on their bodies that were exposed despite the mail chains.
A bullet proof jacket is made from several thin layers of a material known as kevlar ( Kevlar is a registered trade mark). Kevlar is a para-aramid synthetic fibre. Some vests also allow for metal plates to be inserted. While kevlar is light-weight, inserted metal plates make the vest heavier. Though if the vest stops a bullet, I doubt the wearer would mind how heavy the vest was.