Answer
$Br^-$ doesn't act as a weak base.
Work Step by Step
1. Protonate this anion, to get its conjugate acid:
$Br^- --\gt HBr$
2. Analyze the protonated compound.
- Strong acids have insignificant bases as conjugate pair.
- HBr is a strong acid, therefore, $Br^-$ has an insignificant basicity.
- So, $Br^-$ doesn't act as a weak base.