>I assume that dark matter is made of heavy neutrinos.

One of the models for constituents of dark matter uses [supersymmetry][1] with R parity conservation. The corresponding supersummetric partners of neutrinos are called neutralinos n. There are problems with these models and it is a research field.

>But wouldnt they be converted into neutrinos with less mass throygh weak interaction

No ,neutralinos cannot decay because of R parity conservation. 

Neutralinos are beyond the standard model that fits observed particles, so it is a new particle, if it exists.

Everything about dark matter is under research.


  [1]: https://arxiv.org/abs/1701.05259