Question

Why does time slow down near heavy objects?

Answer 1

The effect you're talking about is called gravitational time dilation. The effect is easily calculated from the metric (typically the Schwarzschild metric) but when you ask "why is this?" I'd guess you're asking if there is a way to understand why this happens without working through all the algebra. The answer is no, not really, but I can attempt to give a rough sketch. However note well that this is not an accurate description of the physics and will mislead you if you push it too far. But to do any better does involve diving into the maths.