The Higgs field is a likely candidate for giving particles mass. Furthermore, if the particle interacting with the Higgs field gives it mass, it's then the warping of space-time from the mass that generates gravity. A proton would not meet this criteria.
We know from Isaac Newton and his law of gravitation that any two objects in the Universe exert a force of attraction on each other. This relationship is based on the mass of the two objects and the distance between them. The greater the mass of the two objects and the shorter the distance between them, the stronger the pull of the gravitational forces they exert on each other.