  The kagome metals $A$V$_{3}$Sb$_{5}$ ($A$ = K, Rb, Cs) have attracted
enormous interest as they exhibit intertwined charge-density wave (CDW) and
superconductivity. The alkali-metal dependence of these characteristics
contains pivotal information about the CDW and its interplay with
superconductivity. Here, we report optical studies of $A$V$_{3}$Sb$_{5}$ across
the whole family. With increasing alkali-metal atom radius from K to Cs, the
CDW gap increases monotonically, whereas $T_{\text{CDW}}$ first rises and then
drops, at variance with conventional CDW. While the Fermi surface gapped by the
CDW grows, $T_{c}$ is elevated in CsV$_{3}$Sb$_{5}$, indicating that the
interplay between the CDW and superconductivity is not simply a competition for
the density of states near \EF. More importantly, we observe an enhancement of
electronic correlations in CsV$_{3}$Sb$_{5}$, which suppresses the CDW but
enhances superconductivity, thus accounting for the above peculiar
observations. Our results suggest electronic correlations as an important
factor in manipulating the CDW and its entanglement with superconductivity in
$A$V$_{3}$Sb$_{5}$.
