We compute the weight 2 cohomology of the Feynman transforms of the cyclic (co)operads \(\textsf{BV}\) and \(\textsf{HyCom}\) , and the top \(-2\) weight cohomology of the Feynman transforms of \(D\textsf{BV}\) and \(\textsf{Grav}\) . Using a result of Giansiracusa, we compute, in particular, the top \(-2\) weight cohomology of the handlebody group. We compare the result to the top \(-2\) weight 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.
