(Front page is dated, see publications tab for more recent work) http://www.npl.washington.edu/eotwash/
The most-important experiment we do is to test the Equivalence Principle [1], the idea that if you drop two things in vacuum, they'll fall at the same rate regardless of what they're made from. Results from our lab have shown that, at 1 part in 10,000,000,000,000 (10^-13), that's apparently true. General Relativity takes the Equivalence Principle as a postulate, and works from there. Many theories of new physics would break the EP at scales of ~10^-15 or so.
My almost-complete thesis research is searching for violations of the gravitational inverse square law at short distances. In short, over distances smaller than the diameter of a hair, nobody knows if gravity acts. It probably does, but you don't know until you check. String theory would suggest that, at short-enough distances, gravity should get unexpectedly stronger. Solutions to the Cosmological Constant problem [2] may suggest that gravity should turn off at distances shorter than the diameter of a hair. Dark Energy/Hubble Constant observations would suggest that gravity might do something interesting at around this same scale.
Our workhorse technology is the venerable torsion balance [4], souped-up with modern experimental readout and data analysis techniques. Our best angle sensors [5] sense a nanoradian's angular displacement in less than a second. For scale, if we shine a laser pointer from Seattle to San Francisco, a nanoradian is equivalent to about a millmeter's displacement of the beamspot on the TransAmerica building.
If you want me to build you an angle sensor or a precision force sensor, I'm interested in hybrid industrial and academic work [6].
[1] http://en.wikipedia.org/wiki/Equivalence_principle
[2] http://en.wikipedia.org/wiki/Cosmological_constant
[3] http://en.wikipedia.org/wiki/Dark_energy
[4] http://en.wikipedia.org/wiki/Torsion_spring#Torsion_balance
I'm surprised to read the statement "over distances smaller than the diameter of a hair, nobody knows if gravity acts" as I thought we were accurately measuring all sorts of interactions at or below that scale (10s of microns).
It sounds like a very interesting field to be in!
That said, the geometry of some of the Texas Instruments DLP MEMS chips has interested some of us for years. The chips are designed to be robust in consumer products, but if they instead designed their mirrors to have very soft springs, we'd be interested in playing with them. Once a year or so, I do a survey of the available MEMS accelerometer chips to see if it's worth building an array from them. They're still a few orders of magnitude away in sensitivity from anything we could put to use.
For the second half of your question: Physicists do indeed measure interactions at scales far smaller than the diameter of a proton. The "trouble" with gravity is that it's so very weak. On a handwavy charge-for-charge basis, gravity is 10^40 (that's 10,000,000,000,000,000,000,000,000,000,000,000,000,000) times weaker than electromagnetism. For an experiment that's purely sensitive to electromagnetism (atomic spectroscopy) or other comparably strong forces (particle colliders) to see gravity, it's necessary to resolve the other forces incredibly well in order to see a tiny residual effect from gravity.
For our work, achieving sensitivity to gravity at the scale of tens of microns isn't that hard. Proving to you that we're not seeing another force/experimental influence (the flip side of that 10^40) is very hard, and is what I spend almost all of my time trying to do.
Thanks for your interest; it's sharing the stoke about this stuff that keeps us going when it's hard (and, if you're a US citizen, you're paying for it! Thank you!).
Sorry, not US, Australian. Although I just checked and QUT in Brisbane are apparently doing some good work in microgravity research.
Time to do some reading!