How precise can current technologies measure the mass of an object? Masses of various objects are listed on this wikipedia page: Orders of magnitude (mass). For example, mass of an HIV-1 virus is on the order of 1 femtogram.


*

*Are these data actually measured (which I really doubt), or calculated?

*What is the most precise measurement technique we have to measure the mass of an object?
 A: The most precise measurement of the mass of an electron was reported by Sturm et al in Nature 506, 467–470 (27 February 2014), quoting a relative precision of $3\times 10^{-11}$, meaning they determined the mass to better than $3\times 10^{-41}~\rm{kg}$.
If that is not the best, at least it gives you an upper bound...
Note that if you could weigh such a small mass directly with scales on earth, the force would be equivalent to the gravitational pull of a mosquito (mass 2.5 mg) on a grain of sand (0.7 mg) at a distance of about 6 million kilometers - about 17 times the distance to the moon...
Astonishing.
Acknowledgement: CuriousOne's comment got me thinking about the measurement of the mass of the electron, and led me to the above analysis. 
A: Many of them are calculated.  All the ones that have $u$ or $Da$ as the unit are in atomic mass units, referenced above in the table.  They just count up the atoms and add.  For bacteria, yeast, and the like it will vary from one specimen to another.  Not much precision is quoted and it is likely they use the volume (easy to measure with a photograph) and assume a density like water.
