  We calculate the $\mathcal{O}(\alpha)$ weak corrections to top quark pair
production at the LHC and include anomalous electroweak interactions from
dimension-six operators. The loop calculation and renormalization are
consistently done within the Standard Model Effective Field Theory. Sensitivity
to the involved operators is exposed through the virtual corrections, which
receive enhancement from electroweak Sudakov logarithms. We investigate the
prospects of using this feature for probing New Physics at the LHC that so far
has only been studied in final states with on-shell sensitivity such as
$t\bar{t}+Z$ or $t \to b W$. We find that the large $t\bar{t}$ production rate
and the excellent perturbative control allow compensating the loop suppression
and yield remarkably strong constraints that are competitive with those from
$t\bar{t}+Z$.
