I have heard that neutrinos can only be affected by the Weak Interaction (apart from gravity). How is a neutrino affected by weak interaction? I would like to ask the detail. Are there any relationships between WIMPs and neutrinos for the interaction?
The gravitational and the weak forces are the only interactions that affect all matter, which is made of fermions.
The neutrino has a strong connection to the weak interaction because, being uncharged and very light, it doesn't couple to any of the other three fundamental interactions. If you are asking about the reason as to why this happens, then I am afraid there isn't one. Why are there muons and taus if matter is not made up of them? Neutrinos do seem to be useful though, in particular as far as conservation laws are concerned: for example, a large fraction of the Sun's energy is radiated in the form of neutrinos, which needs to be taken into account when computing the energy output of our star (see here).
A more important role played by neutrinos is the following:
Wolfgang Pauli theorised their existence after the observation of the neutron decay: what they saw was a neutron (uncharged, half-integer spin) decaying into an electron (charged -1, half integer spin) and into a proton (charged +1, half integer spin). Although charge was conserved, this decayed violated the conservation of lepton number, and the spins did not add up correctly (two half integer spins add to an integer). So the neutrino (or in this particular case an antineutrino) was predicted as a uncharged lepton, with half integer spin. (EDIT: what I said is true, but it is not actually the real reason why the neutrino was first postulated: the spectrum (distribution) of the energies of the positron was continuous, which did not agree with the expected spectrum for a two-body decay. So they needed an extra particle that the positron could have splitted the energy with). By the way, this is how the neutrinos that come from the Sun are created: during nuclear fusion, a proton turns into a neutron thus releasing a neutrino.
And yes, there is a relationship with WIMPs. WIMPs (Weakly Interacting Massive Particles) are the hypothetical constituents of dark matter. As you may know, dark matter does not seem to interact via electromagnetic interaction (it's dark, it does not emit light). It should interact via the gravitational force, which is actually the very reason why dark matter was invented in the fist place, to explain why sometimes there seems to be a much greater gravitational field than the one caused by visible matter. If it interacted via the weak force, as all matter does, then we could devise experiments that would shed some light on its constituents.