  We study the superfluid weight $D^s$ and Berezinskii-Kosterlitz-Thouless
(BKT) transition temperatures $T_{BKT}$ in case of exotic Fulde-Ferrell (FF)
superfluid states in lattice systems. We consider spin-imbalanced systems with
and without spin-orbit coupling (SOC) accompanied with in-plane Zeeman field.
By applying mean-field theory, we derive general equations for $D^s$ and
$T_{BKT}$ in the presence of SOC and the Zeeman fields for 2D Fermi-Hubbard
lattice models, and apply our results to a 2D square lattice. We show that
conventional spin-imbalanced FF states without SOC can be observed at finite
temperatures and that FF phases are further stabilized against thermal
fluctuations by introducing SOC. We also propose how topologically non-trivial
SOC-induced FF phases could be identified experimentally by studying the total
density profiles. Furthermore, the relative behavior of transverse and
longitudinal superfluid weight components and the role of the geometric
superfluid contribution are discussed.
