Question

why any body exerts gravitational field on other bodey?

Answer 1

At one level, this is just a law of physics and you just have to accept. Is it obvious? No. But has every experiment we've ever done shows that it is the case? Yes.

At another level, this is a very deep question and part of the experiments right now at CERN are designed to try and get to the bottom of it, looking for the way that matter "tells" other matter it has mass. The mechanism for doing so is a theoretical particle called the Higgs Boson. Experiments right now are designed to try and observe it explicitly.