We have a beautiful weeping willow that is wreaking havoc everywhere. It grew incredibly fast and its roots are traveling into neighbors yards, which makes them very unhappy. We lose a lot of limbs in storms. Our 2 choices, remove beautiful tree which will cost close to $1800, or have roots cut back.
Willows are noted for fast growth, brittle branches, vigorous root systems and being attacked by many diseases and insects. They will grow new branches from old wood and their roots will seek water where ever they can grow. You cannot change these characteristics but managing them brings it's own issues.
You can get it removed and consider replanting with a more suitable tree which is another question or you can manage it.
Management would consist of yearly root and branch pruning. In fact, coppicing or pollarding would work quite well. Get the tree cut down to the ground or down to four or five feet and then every year prune the new growth back.
To control the roots you need to cut a trench about a foot deep along your property line and line it with an impervious membrane like an EPDM 60 mm pool liner. Back fill the trench and inspect yearly to see if any roots are going under it.
This could be more work on a yearly basis than just cutting it down but it depends how much you want to keep the tree.