We report a new measurement of parity nonconserving (PNC) optical rotation near the 1.28 $\ensuremath{\mu}$m, ${6P}_{1/2}\ensuremath{\rightarrow}{6P}_{3/2}$ magnetic dipole transition in thallium. We find the ratio of the PNC $E1$ amplitude to the $M1$ amplitude to be $R\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}(\ensuremath{-}14.68\ifmmode\pm\else\textpm\fi{}0.17)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}$, which within the present uncertainty of atomic theory yields the thallium weak charge ${Q}_{w}(^{205}T\mathrm{l})\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{-}114.2\ifmmode\pm\else\textpm\fi{}3.8$ and the electroweak parameter $S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{-}2.2\ifmmode\pm\else\textpm\fi{}3.0$. Separate measurements on the $F\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$ and $F\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$ ground-state hyperfine components of the transition yield ${R}_{1}\ensuremath{-}{R}_{0}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}(0.15\ifmmode\pm\else\textpm\fi{}0.20)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}$, which limits the size of nuclear spin-dependent PNC in Tl.