Neutrino is affected by weak subatomic force and gravitational force and just like dark matter they don't easily interact with matter, if dark matter cannot be affected by the weak interaction how else can we detect its presence aside from the distortion of light in its vicinity?
We need to distinguish between the concept of Dark Matter and the potential candidates that fill it's role. Dark matter, as originally posited, was just non-luminous matter that could be inferred only through gravity.
As time went on, additional research shed more light on what dark matter was. Both the growth of large scale structure of the universe and Big Bang Nucleosynthesis showed that the majority of dark matter had to be non-baryonic. Baryons are particles made up of quarks (ie protons and neutrons), so most dark matter has to be something that doesn't exist in the standard model.
Many candidates are proposed for non-baryonic matter. When you refer to the weak force, you are referring to a WIMP which is one particular candidate. This was motivated by the so-called WIMP miracle: the dark matter density observed implied that dark matter particles should occur at the weak scale and particle physics had problems that could be helped with a particle at the weak scale. So to kill two birds with one stone, a WIMP is theorized. However, there is no experimental evidence to actually justify this theory.
If it's not correct, there are many other theories that could explain dark matter. Probably the second most common particle for Dark Matter is the Axion. This Goldstone Boson was proposed to solve the Strong CP violation.
Of the three generation 2 dark matter proposals recently approved in the US, two (LUX and CDMS) search for WIMPS, while ADMX is focused on the Axion. However, neither candidate has any actual experimental evidence. And many other candidates are frequently proposed.