  For any quasi de Sitter background, we show that a recently proposed scalar
weak gravity conjecture (sWGC) follows from the swampland distance conjecture,
together with the covariant entropy bound. While pointing out the limitations
of our argument, we suggest how further generalizations of our result might
indicate that the shape of the potential of a scalar field in a low-energy
effective field theory gets highly constrained due to the distance conjecture
alone, going beyond the refined de Sitter conjecture. We also correct some
previous comments regarding cosmological implications of the sWGC.
