If the Higgs gives mass, wouldn't the Higgs give gravity too? If it exists that is.
Not necessarily, although we may eventually run into difficulties, one could imagine a world in which gravitation would be so weak that a civilization has developed the same standard model (of elementary particles) as ours, and in this theory the Higgs boson only provides inertial mass, in fact the model says nothing about gravity. Plus, we are talking about current mass, not even the observed inertial mass of atoms around us (and in particular the generation of hadronic masses).
This being said, there are attempts to link the Higgs mechanism with gravity, however those are very speculative and tenuous links.
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