Since the foundational work of Broadhurst and Kreimer, there has been a significant push to understand the amplitudes of Feynman Integrals as periods, or integrals of algebraic functions over algebraic domains. Work of Brown has related these periods to the homology of Kontesevich's graph complex, and therefore the cohomology of the moduli space of curves by work of Chan, Galatius and Payne. Central to the story are the Borel classes - GLn(Z) equivariant cohomology classes on the space of projective symmetric matrices of full rank. I first show that, in a very general setting, the Voevodsky motive of this space splits into a direct sum of Tate Motives. I conclude by work in-progress with collaborators, where we aim to compute the weights of the Borel classes viewed as differential forms on the space of projective complex symmetric matrices of full rank and use this computation for the study of multiple zeta values.