Can we weight dark matter? We can observe the effect of light as it gets bended in the presence of dark matter, and I wonder how is it possible to measure their mass given that we can't see them and they don't interact with ordinary matter? I know because the speed of the stars at the edge and the center of our galaxy give us a hint that dark matter is presence but I want to know if we can directly measure their mass?
For example LIGO is used to detect gravitational wave and can even pin point the source, super kamiokande mostly used to find neutrino which tell us the direction of the supernovae, etc.
 A: By definition of dark matter, it is not possible to determine specific masses with astrophysical means, only the gravitational effect they have. The masses may be composed of various things, as this table shows.
For example the machos will not have distinctive masses , they would be planet like,

A massive astrophysical compact halo object (MACHO) is any kind of astronomical body that might explain the apparent presence of dark matter in galaxy halos. A MACHO is a body composed of normal baryonic matter that emits little or no radiation and drifts through interstellar space unassociated with any planetary system. Since MACHOs are not luminous, they are hard to detect.

So it is an open question for various models.
Models that have to do with particle physics are the only ones where a mass could be given by experiment. They are particles called  WIMPS which are searched methodically in accelerator experiments, because they are predicted by supersymmetric and other models, so if they are found it would be a success for the models and for having candidates of dark matter, to be used in cosmological models.
It is an open research field, as the table shows.
