What size particle would be attracted to this 340 ton sculpture's gravitational field? I know that gravity is a weak force, but this rock has mass, so it has gravity. The Levitated Mass sculpture is big enough to attract something. What is the largest particle that would "stick" to the underbelly of this sculpture because of its gravitational attraction? 
I am interested in this sculpture because you can walk right under it! If the particle is big enough to see in a microscope, seems like this would be a great experiment for the youngins.
 A: This experiment is bound to fail, because a particle underneath the large mass will still be feeling the force of mg of the earth. The attraction of the large mass will have an upward force of (m_1xm_2/r^2)xG .

From the value of the gravitational constant one sees that the equivalent "g" for the attraction of the levitating mass is very small for 340 tons to overcome the force of earth gravity.
A: As many here have noted, Earth poses a problem for your experiment.
So, let's remove it$^\dagger$.
You now have a freely floating rock in space of mass $M = 3.4\times10^8\,\mathrm{g}$ and radius $R = 330\,\mathrm{cm}$.
The escape velocity of the rock is
$$v_\mathrm{esc} = \sqrt{\frac{2GM}{r}},$$
where $r$ is the distance to the center of the rock, i.e. $r\gtrsim R$. This evaluates to at most $37\,\mathrm{cm}\,\mathrm{s}^{-1}$.
The typical speed of a particle of mass $m$ at a gas temperature $T$ is
$$v_\mathrm{rms} = \sqrt{\frac{3 k_\mathrm{B}T}{m}},$$
where $k_\mathrm{B}$ is Boltzmann's constant. Since we've removed Earth, the temperature is given by the interplanetary medium at a distance of 1 AU from the Sun, which is of the order 100–200 K. 
What this means is that the answer is not a "most massive particle", but a "least massive particle", corresponding to how close the particles can come to the rock, i.e. $r=R$. The result is
$$m = \frac{3 k_\mathrm{B} T r}{2 G M} \simeq 5\times10^{-13}\,\mathrm{g}.$$
This is not a lot, but much more massive than atoms or normal molecules. It would probably be classified as a "large dust grain"

$^\dagger$Removing Earth is left as an exercise for the reader.
