gravity - What is the smallest particle exhibiting gravitational properties?

I've long been taught that all matter having mass, possesses attractive forces somewhat akin to gravity. As such, imagine we can 'teleport' a gravitonic detection device that can accurately measure the gravitational forces regardless of strength present at each location, it can detect all gravitational forces ordered by direction of pull within a given radius of up to let say [through a range of settings/switches of 0.001 nanometer to 100,000 km. We teleport these detectors equi-distantly apart in the earth, from troposphere to molten mantle to core's center of mass. measure and plot all the forces detected. Supposedly, there is no gravity at earths center of mass...that means gravity can be concentrated and nullified. Logic tends to indicate 'no gravity=no weight. Therefore why does all reference material say massive objects have tremendously large core pressures and squeeze atoms to extremely dense masses. If gravity is nullified, what is source of this crushing, without usurping all gravitational common sense?