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The problem is that the Higgs field only describes how some inertial mass comes into being (some can come from bound energy--for example, a proton gets a lot of its mass from the binding energies of its constituent quarks). The force of gravity depends on gravitational mass. So far as we can tell the two are equivalent, but we don't have a mechanism that explains why they're equivalent. Presumably, if you figured out the mechanism, you'd know how the two are related and what relationship the Higgs field has to gravity. It would probably also answer a lot of questions about quantum gravity.