  We analyse FORS2/VLT $I$-band imaging data to monitor the motions of both
components in the nearest known binary brown dwarf WISE J104915.57-531906.1AB
(LUH16) over one year. The astrometry is dominated by parallax and proper
motion, but with a precision of $\sim$0.2 milli-arcsecond per epoch we
accurately measure the relative position change caused by the orbital motion of
the pair. This allows us to directly measure a mass ratio of $q=0.78\pm0.10$
for this system. We also search for the signature of a planetary-mass companion
around either of the A and B component and exclude at 3-$\sigma$ the presence
of planets with masses larger than $2\,M_\mathrm{Jup}$ and orbital periods of
20--300 d. We update the parallax of LUH16 to $500.51\pm0.11$ mas, i.e. just
within 2 pc. This study yields the first direct constraint on the mass ratio of
LUH16 and shows that the system does not harbour any close-in giant planets.
