  Site-dependent local spin susceptibility is investigated with $^{125}$Te
nuclear magnetic resonance in a Weyl semimetal WTe$_2$. The nuclear
spin-lattice relaxation rate $1/T_1T$ shows a dependence of the square of
temperature $T$ at high temperatures, followed by a constant behavior below 50
K. The temperature dependence features Weyl fermions appearing around the
linearly crossing bands. The Knight shift $K$ scales to the square root of
$1/T_1T$, corroborating a predominant spin contribution in low-lying
excitation. The observed dependence of $K$ and $1/T_1T$ on the four Te sites
shows the site-dependent electron correlation and density of states. The
angular profile of the NMR spectrum gives the anisotropic hyperfine coupling
tensor, consistent with $5p$ hole occupations on Te sites.
