are you growing an actual; weeping willow? Or a regular willow that you want to wire in a weeping form?
In any case, one can wire branches as soon as they are there. I wire my deciduous trees in early spring before the new branches turn woody, and unwire a few weeks later. Then I let them grow, trim back at the end of spring and do the same thing once more. That I let grow till fall. In fall at leaf drop I normally try to trim and wire once more.
All dependent on how the individual tree responds.
Do not wire trees that are still rooting. Only wire established plants (Repotted is fine)