gravity - How can the core of the Earth be younger than the crust due to gravitational time dilation if the crust experience more force than the core?

Gravitational force decreases with depth under the surface of Earth, and at centre, the surrounding forces cancel each other out effectively making it zero and hence a body at the center of gravity of the Earth (which would be very close to the centre of the Earth, the core) would experience weightlessness. Now the famous study in 2016 (https://arxiv.org/abs/1604.05507) says that the core is 2.5 years younger than the crust even though the former was formed first, due to gravitational time dilation causing the core to age slower even though the gravity acting on the core should be lower than what is on the crust. I understand that I might be confusing myself between two scientific principles but I want to understand both and know where my understanding is wrong.