Large anomalous Hall effect induced by weak ferromagnetism in the noncentrosymmetric antiferromagnet <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi mathvariant="normal">CoNb</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">S</mml:mi><mml:mn>6</mml:mn></mml:msub></mml:math>

We study the mechanism of the exceptionally large anomalous Hall effect (AHE) in the noncentrosymmetric antiferromagnet $\mathrm{Co}\mathrm{Nb}_3\mathrm{S}_6$ by angle-resolved photoemission spectroscopy (ARPES) and magnetotransport measurements. From ARPES measurements of $\mathrm{Co}\mathrm{Nb}_3\mathrm{S}_6$ and its family compounds ($\mathrm{Fe}\mathrm{Nb}_3\mathrm{S}_6$ and $\mathrm{Ni}\mathrm{Nb}_3\mathrm{S}_6$), we find a band dispersion unique to the Co intercalation existing near the Fermi level. We further demonstrate that a slight deficiency of sulfur in $\mathrm{Co}\mathrm{Nb}_3\mathrm{S}_6$ eliminates the ferromagnetism and the AHE simultaneously while hardly changing the band structure, indicating that the weak ferromagnetism is responsible for the emergence of the large AHE. Based on our results, we propose Weyl points near the Fermi level to cause the large AHE.