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