Why is the vertical part of a titration curve longer for a strong acid by a strong base than for a weak?
Compare (1) the titration of $\ce{NaOH}$ with $\ce{HCl}$ and (2) that of $\ce{NaOH}$ with $\ce{AcOH}$.

At the equivalence point of each titration, solution (1) contains $\ce{Na+}$, $\ce{Cl-}$, and $\ce{H2O}$, with negligible concentration of $\ce{H+}$ and $\ce{OH-}$. In contrast, solution (2) contains $\ce{Na+}$, $\ce{AcO-}$, and $\ce{H2O}$, and in particular $\ce{AcO-}$ will react with water to form a buffer solution of $\ce{AcO-/AcOH}$.

This will be true in general for any weak acid/base titration. The resulting buffer resists changes in pH; hence a weak-acid titration curve is not as steep at the equivalence point as is a strong-acid titration curve.