House of Wax --
Wow, that is a really bad weed forest going on over there..
I am sorry you have to see it and deal with it on YOUR side..
Your guys will have to really keep up on weed and feed, pre and post - emergent applications, to fight all the weed seeds that are constantly coming over into your yard..
I hope they know what they are doing..
Totally agree, you need to make a visit, and tell them your guys are going to have to use stuff to keep their weeds out of your yard. It might overlap from time to time..
Hopefully, they will take that cue and get some products down on their yard..
All you can do.. Sorry... I hope you can find a good solution.. Perhaps the only/best solution will be to put up a 6` tall nice wooden fence on or close to the Property Line, and that for sure will help slow the weed seed migration down..
What I personally would do is really grow my grass thick and high, and keep it going really strong to help combat all those seeds that are going to get into it anyway from their side..
Things that can help your soil become better soil is of course, aerating perhaps twice a year, putting down seed, fertilizer, and other amendments when done, and watering all in really well.. Sometimes if the lawn gets too thick with excess thatch, that needs to be removed as well..
I have been lately studying up on Humic Acid which is something natural that is mined from I believe shale deposits, up in the mountains.. It is said that this product in the correct configuration will break down very quickly and add a lot of beneficial organisms and things into your soil and eventually, your soil can be improved..
Once your soil is working really good under there, it just keep getting better and of course whatever is growing above it gets much healthier too..
One such company out of Maumee, Ohio, seems to be really doing good with this product - check it out here, the product is called Anderson Humic DG Here is the link to the company in Ohio --
https://andersonshumates.com/
Good luck with this ! I know you will do just fine !
Dan F