The conjugate bases of most weak acids are weak bases.
The only conjugates that are strong bases are those of extremely weak acids, like water (pKa = 14), for which OH- is the conjugate base.
"The conjugate base of a relatively weak weak acid is a relatively strong weak base, and the conjugate base of a relatively strong weak acid is a relatively weak weak base."
NH2- is the conjugate base of an extremely weak acid, NH3 (pKa = 35). On the otehr hand, CN- is the conjugate base of a moderately weak acid, HCN (pKa = 9.2), so it's a moderately weak base.
