We report on muon spin rotation experiments probing the magnetic penetration depth λ(T) in the layered superconductors in 2H-NbSe₂ and 4H-NbSe₂. The current results, along with our earlier findings on 1T′-MoTe₂ (Guguchia et al.), demonstrate that the superfluid density scales linearly with T_c in the three transition metal dichalcogenide superconductors. Upon increasing pressure, we observe a substantial increase of the superfluid density in 2H-NbSe₂, which we find to correlate with T_c. The correlation deviates from the abovementioned linear trend. A similar deviation from the Uemura line was also observed in previous pressure studies of optimally doped cuprates. This correlation between the superfluid density and T_c is considered a hallmark feature of unconventional superconductivity. Here, we show that this correlation is an intrinsic property of the superconductivity in transition metal dichalcogenides, whereas the ratio T_c/T_F is approximately a factor of 20 lower than the ratio observed in hole-doped cuprates. We, furthermore, find that the values of the superconducting gaps are insensitive to the suppression of the charge density wave state.