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Starting with some known localization (matrix model) representations for
correlators involving 1/2 BPS circular Wilson loop $\cal W$ in ${\cal N}=4$ SYM
theory we work out their $1/N$ expansions in the limit of large 't Hooft
coupling $\lambda$. Motivated by a possibility of eventual matching to higher
genus corrections in dual string theory we follow arXiv:2007.08512 and express
the result in terms of the string coupling $g_{\rm s} \sim g^2_{\rm YM} \sim
\lambda/N$ and string tension $T\sim \sqrt \lambda$. Keeping only the leading
in $1/T$ term at each order in $g_{\rm s} $ we observe that while the expansion
of $\langle {\cal W} \rangle$ is a series in $g^2_{\rm s} /T$, the correlator
of the Wilson loop with chiral primary operators ${\cal O}_J $ has expansion in
powers of $g^2_{\rm s}/T^2$. Like in the case of $\langle {\cal W} \rangle$
where these leading terms are known to resum into an exponential of a
"one-handle" contribution $\sim g^2_{\rm s} /T$, the leading strong coupling
terms in $\langle {\cal W}\, {\cal O}_J \rangle$ sum up to a simple square root
function of $g^2_{\rm s}/T^2$. Analogous expansions in powers of $g^2_{\rm
s}/T$ are found for correlators of several coincident Wilson loops and they
again have a simple resummed form. We also find similar expansions for
correlators of coincident 1/2 BPS Wilson loops in the ABJM theory.