Does gravitation really exist at the particle level? As I understand, we usually talk about gravity at a macro scale, with "objects" and their "centre(s) of mass". However, since gravity is a property of mass generally (at least under the classical interpretation), it should therefore apply to individual mass-carrying particles as well.
Has this ever been shown experimentally? For example, isolating two particles in some manner and then observing an attraction between them not explained by other forces.
To pose the question another way, let's say I have a hypothesis that gravitation is only an emergent property of larger systems, and our known equations only apply to systems above some lower bound in size. Is there any experiment that reasonably disproves this hypothesis?
 A: For the interaction of one small (atom scale) mass and one large mass, measurements of the Earth's atmosphere that anyone could do with a homemade barometer and a nearby mountain constitute direct experimental confirmation. We find more gas molecules at low altitudes than at high altitudes. Only gravity acting on each gas molecule independently could be responsible for the observed behavior - they behave like a gas, but they don't just float away and uniformly distribute themselves across the cosmos, but instead assemble themselves into a pressure gradient pointing towards the center of the planet.
For the interaction of two small masses, rather than one small mass and Earth, or large distributions of small masses (e.g. nebula formation), the smallest I've read about is this one from last year, using ~90mg gold spheres. See arXiv: 2009.09546 [gr-qc].
A: Here is an easy way to grasp how difficult it would be to make the direct measurement you propose.
Take two protons and place them one centimeter apart. They will exert a certain tiny amount of gravitational attraction, which we measure by some magic means, and a certain amount of electrostatic repulsion, which we will also measure.
Now, how far apart would we need to separate those two protons in order for the strength of the electrostatic force they experience to diminish to the point where it is as weak as the gravitational force they experience when they are one centimeter apart? Answer: 1.8 light years.
This means that when performing experiments where we have to account for electrostatic forces between individual subatomic particles, those forces will be stronger than the gravitational forces between them by a factor of (1.8 light years/1 centimeter).
And that means that we have no hope of ever, ever directly measuring the force of gravitational attraction between two protons in an experiment: the electrostatic force will utterly overwhelm that experiment.
A: FWIW, small particles react to the big ones:Experiments have been done with neutrons in a gravity field. The phase of their wavefunction was shifted, as was shown by interference. If the neutron didn't have it's own gravity field, would it react? Would an electron without charge accelerate in an electric field? Food for thought.
A: That's exactly what we are observing when we look at the night sky and see galaxies form out of nothing but dust.
Ever wondered why we are here to ask this question? Because gravity pulled together nothing really just dust of particles in the very early universe, forming all the galaxies and solar systems etc.
As a side note, if gravity would not exist at the particle level, this would make it very hard to explain the dark matter halos around the galaxies, since these particles only interact via gravity.

Since the dark matter does not dissipate as it only interacts gravitationally, it remains distributed outside the disk in what is known as the dark halo.

https://en.wikipedia.org/wiki/Galaxy_formation_and_evolution
So at the particle level, the existence of complex (gravitationally bound) systems is the very proof that gravity (understanding how it binds simple dust of particles) really works at the particle level.
A: Mass Spectrometer
I don't recall the formal name for the instrument but I was able to tour a lab at Ohio State University that had mass spectrometers that lofted ionized individual molecules a few feet up a column and waited for them to pass a detector as they fell due to gravity. Organic molecules aren't quite point masses but they are about as close as you can reliably get measurements for. The instrument was considered to be best in class at the time and this was only a few years ago.
