Using supersymmetric localization, we study the sector of chiral primary operators (Tr ϕ 2 ) n with large R -charge 4 n in $$ \mathcal{N} $$ N = 2 four-dimensional superconformal theories in the weak coupling regime g → 0, where λ ≡ g 2 n is kept fixed as n → ∞, g representing the gauge theory coupling(s). In this limit, correlation functions G 2 n of these operators behave in a simple way, with an asymptotic behavior of the form $$ {G}_{2n}\approx {F}_{\infty}\left(\uplambda \right){\left(\frac{\uplambda}{2\pi e}\right)}^{2n} $$ G 2 n ≈ F ∞ λ λ 2 π e 2 n n α , modulo O (1 /n ) corrections, with $$ \alpha =\frac{1}{2} \dim \left(\mathfrak{g}\right) $$ α = 1 2 dim g for a gauge algebra $$ \mathfrak{g} $$ g and a universal function F ∞ (λ). As a by-product we find several new formulas both for the partition function as well as for perturbative correlators in $$ \mathcal{N}=2\kern0.5em \mathfrak{s}\mathfrak{u}(N) $$ N = 2 s u N gauge theory with 2 N fundamental hypermultiplets.