Recent experiments have demonstrated interesting physics in a family of two-dimensional composition-tunable materials ${\mathrm{Nb}}_{2n+1}{\mathrm{Si}}_{n}{\mathrm{Te}}_{4n+2}$. Here we show that, owing to their intrinsic low symmetry, metallic nature, tunable composition, and ambient stability, these materials offer a good platform for studying the Berry curvature dipole (BCD) and nonlinear Hall effect. Using first-principles calculations, we find that the BCD exhibits pronounced peaks in monolayer ${\mathrm{Nb}}_{3}{\mathrm{SiTe}}_{6}$ (the $n=1$ case). Its magnitude decreases monotonically with $n$ and completely vanishes in the $n\ensuremath{\rightarrow}\ensuremath{\infty}$ limit. This variation manifests a special hidden dimensional crossover of the low-energy electronic states in this system. The resulting nonlinear Hall response from the BCD in these materials is discussed. Our work reveals pronounced geometric quantities and nonlinear transport physics in ${\mathrm{Nb}}_{2n+1}{\mathrm{Si}}_{n}{\mathrm{Te}}_{4n+2}$ family materials, which should be readily detected in experiment.