We present preliminary results on the susceptibilities involving the CP-violating (CPV) Weinberg three-gluon operator and the topological Θ term using the gradient flow scheme, and study their continuum and chiral extrapolations. These are used to provide an estimate of the Θ induced by the Weinberg operator in theories with the Peccei-Quinn (PQ) mechanism. Combined with the calculations of the matrix elements (MEs) of quark-bilinears between nucleon states, such calculations will enable estimates of the electric dipole moments (EDMs) and CPV pion-nucleon couplings due to the Weinberg operator, thereby providing robust constraints on beyond the standard model (BSM) physics.