Never heard of it. Yes the previous owner picked the worst place to plant any tree aside from close to a house. My advice to you is to trim away any branches against or over the fence on a continual basis always making sure the tree height never gets taller than the fence or it will get out of hand. Remember, keep at it and never slack off trimming this tree. Otherwise, consider removing it. Welcome to GOY and thank you for the photo of your problem.

That does look like Salix babylonica, the classic weeping willow seen usually in parks, so unless you know its a dwarf variety of some sort, I'd have it removed asap - these trees are rapid growers and get very large indeed (height around 60 feet, spread 30-40 feet), and, like many willows, they like damp/wet places, so their roots often invade drains and sewers. Given you apparently live in a built up area with other residences nearby, its quite possibly one of the worst choices ever for a garden tree. I wouldn't want to risk leaving it not only because its size will be impossible to control, but also because of the risk of insurance claims later from surrounding properties.

Good previous advice. This is certainly a tree not to have in your back garden unless you live in a park. If you leave it, it will come back to bite you.

Willows are lovely and the weeping ones especially so, but just to add to the warnings above - we live in an area where the land moves! It really does and along the road is a weeping willow which the Council have spend thousands of pounds on repairing the road. It sucks all the water out of the land and the road drops, huge dip in the road, massive road works to sort it out (has been done several times), this time it's cured it for longer than usual, but it's starting to have a dip again!
So if it's close to anyone's house - beware!