We report on a new measurement of the parity-violating asymmetry in quasielastic electron scat- tering from the deuteron at backward angles at Q2 = 0.038 (GeV/c)2. This quantity provides a de- termination of the neutral weak axial vector form factor of the nucleon, which can potentially receive large electroweak corrections. The measured asymmetry A = −3.51 ± 0.57 (stat) ± 0.58 (sys) ppm is consistent with theoretical predictions. We also report on updated results of the previous experiment at Q2 = 0.091 (GeV/c)2, which are also consistent with theoretical predictions.