We compute the weight 2 (resp.~top−2) cohomology of the Feynman transforms of the cyclic (co)operads BV, DBV, Grav and HyCom. Using a result of Giansiracusa we compute in particular the weight top−2-cohomology of the handlebody group. We compare the result to the weight top−2 cohomology of the moduli space of curves \mathcal M_{g,n}, recently computed by Payne and the last-named author. We also provide another proof of a recent result of Hainaut--Petersen identifying the top-weight-cohomology of the handlebody group with the Kontsevich graph cohomology.
