Rest mass is a fixed quantity inherent to the object), weight changes based on the environment/reference frame -- your weight is different on the moon, but your mass is the same.
Matter is just perturbations in a variety of fields that have complex interactions with each other -- those interactions are what give rise to mass. the higgs field is one of the fields that create mass, most importantly in electrons, but when you measure the mass of any full sized object, almost all of the mass has nothing to do with the higgs field and has to do with the fact that protons are actually balls of quarks and gluons moving very rapidly in a confined space because of their self interactions.
(But well, there's a "then explain gravity!" that you can throw at any generic explanation.)