How can a weak base act as a strong nucleophile (and vice versa)?

1. Carboxylate ion ($\ce{RCOO-}$) is a weak base as the negative charge on oxygen is delocalised due to resonance. So, it has less tendency to donate lone pair of electrons to H+ ion. Similarly, it has less tendency to donate lone pair of electrons to a carbocations. But in my textbook, it is given that, it acts as a weak base but strong nucleophile. Why does it act as strong nucleophile?
2. LDA (lithiumdiisopropylamide) is a strong bulky base. Why it is considered as a weak nucleophile?


