Heavy water is heavy because the hydrogen in it weighs twice as much as ordinary hydrogen (it has a proton and a neutron in its nucleus, instead of just a proton).
Heavy water gets its name because it contains deuterium, a form of hydrogen that has a neutron in its nucleus as well as the usual proton and thus weighs twice as much as the ordinary sort.
The departing halide extracts a proton from the second water and the generated hydroxyl ligand reacts with the ethylene, while remaining in the coordination sphere of the metal.