  In this paper we study the KPZ line ensembles under the KPZ scaling. Based on
their Gibbs property, we derive quantitative local fluctuation estimates for
the scaled KPZ line ensembles. This allows us to show that the family of scaled
KPZ line ensembles is tight. Together with the recent progress in [QS20],
[Vir], and [DM], the tightness result yields the conjectural convergence of the
scaled KPZ line ensembles to the Airy line ensemble.
