  We have systematically investigated the optical conductivity spectra of
La$_{2-2x}$Sr$_{1+2x}$Mn$_{2}$O$_{7}$ ($0.3 \leqslant x \leqslant 0.5$). We
find that just above the magnetic ordering temperatures, the optical gap shows
an enhancement up to $\sim 0.3$ eV near $x=0.4$. Based on a $x$-dependent
comparison of the nesting vector of the hypothetical Fermi surface and the
superlattice wave-vector, we suggest that the peculiar $x$-dependence of the
optical gap can be understood in terms of charge and lattice correlation
enhanced by the charge density wave instability in nested Fermi surface.
