We analyze 67 heavy-ion fusion reactions with high-quality sub-barrier excitation functions using the single-Gaussian model of Jiang et al. [Phys. Rev. C 112, 034612 (2025)] and extract the barrier parameters $R_g,V_g,W_g,R_g^2{W}_g$. The reactions involve seven projectiles, ${}^{16,18}\mathrm{O}, {}^{28,30}\mathrm{Si}, {}^{32,34}\mathrm{S}$, and ${}^{40}\mathrm{Ca}$, on targets from ${}^{12}\mathrm{C}$ to ${}^{208}\mathrm{Pb}$. The mean barrier height $V_g$ scales linearly with $\eta =Z_1{Z}_2/(A_1^{1/3}+A_2^{1/3})$ ($r=0.999$), while $R_g^2{W}_g$ correlates strongly with $W_g$ ($r=0.95$). The $\eta$ dependence accounts for 45% of the variation in fusion strength. After removing this geometric dependence, the resulting structure ratio $r_{\eta }$ shows no correlation with static target deformation or neutron-transfer $Q$ value. For the 24 systems with at least one open transfer channel, however, $r_{\eta }$ correlates strongly with an effective transfer coupling strength $\mathrm{\Lambda }$ ($r=0.70, p=1.4\times {10}^{-4}$), whereas the $Q$ value alone does not. Thus, positive-transfer $Q$ values are necessary but not sufficient for fusion enhancement, with the transfer coupling strength playing a key role. Systems showing the largest deviations from the geometric trend provide promising candidates for detailed coupled-channels studies.

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• Low & intermediate energy heavy-ion reactions
• Nuclear fusion
• Nuclear reactions