Snailrider

Hi Experts, I'm trying to understand the Higgs boson and Higgs Field which, allegedly, is responsible for giving mass to matter. And if the field is all around the universe, why then the same matter weighs different in different gravitational environment (same thing is lighter on Moon etc). You can say, must be because the gravity, but then my question how the Higgs field and gravity (which is based on the mass of object) related?