  We calculate one-loop (purely) Weak (W) corrections of ${\cal
O}(\alpha_{\mathrm{S}}^2\alpha_{\mathrm{W}})$ to the partonic cross section of
two jets at Tevatron and prove that they can be larger than the tree-level
${\cal O}(\alpha_{\mathrm{S}}\alpha_{\mathrm{EW}})$ and ${\cal
O}(\alpha_{\mathrm{EW}}^2)$ Electro-Weak (EW) ones. At high transverse energy
of the jets, all such corrections may lead to detectable effects of, e.g., -10%
or so, with respect to the leading-order (LO) QCD term of ${\cal
O}(\alpha_{\mathrm{S}}^2)$, for the highest value so far probed by Run 2,
depending on the factorisation/renormalisation scale. Besides, they increase
significantly with jet transverse energy. Hence, our results show that EW
corrections may be needed to fit the Standard Model (SM) to present and future
Tevatron jet data.
