We do precision tests of gravity and searches for forces weaker than gravity.
(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
[5] http://arxiv.org/abs/1309.4828
[6] http://www.nanoradian.com