A wire elongates by $\ell \text{mm}$ when a load $W$ is hanged from it. If the wire goes over a pulley and two weights $W$ each are hung at the two ends, the elongation of the wire will be (in mm):

In the first case, the tension in the wire is $T=W$. Elongation $\Delta L=\frac{TL}{AY}$.In the second case, for a massless string over a frictionless pulley with two $W$ loads, the system is in equilibrium. The tension $T$ at any point in the wire is still $W$ (since $T-W=0$).Since the tension $T$ and the material/area are the same, the elongation remains $\ell$.