[sheblindedmewithscience]

In terms of Lewis acids and bases, I don't understand the difference between nucleophiles and bases. Specifically, when one goes down the periodic table, the stability of the leaving group increases, due to the larger size, making that leaving group a weaker base. However, as one goes down the periodic table, the nucleophilicity increases, due polarizability, as the ions get larger.

Would that mean that if one compared two leaving groups going down the periodic table, the one with the larger size (more towards the bottom of the periodic table in the same group) would be a good nucleophile, but a weak base? This doesn't make sense. Could someone explain this in terms of Lewis acids and bases?

[Babcock_Hall]

You are asking a multi-faceted question.  I only feel up to tackling a small fraction of it tonight.  Whether something is a strong base or a weak base is a thermodynamic question; whether something is a strong nucleophile or a weak nucleophile is a kinetic one.  A second thing to bear in mind is that many nucleophiles are Lewis bases, but not all nucleophiles are.