Had a simular problem in 1999.
We had been in my current abode a few years
My property line with my neighbor was lined with large white pines.
About half were rooted on my side.
Everytime we had a storm, large branches would fall on my roof.
I approached my neighbor and asked about splitting the costs for removal/pruning.
He wasn't interested.
Then hurricane Floyd came threw and knocked 2 of them down.
One slicing thru my electric service.
Took 3 days to repair
I called the Town and was told they couldn't force my neighbor to deal with the trees.
So I hired a tree guy who took down all the trees rooted on my property and pruned ALL the branches on my side.
This took all the weight off my side and made the trees lean toward my neighbors property.
A year later.
A big storm downed one of HIS trees and smashed thru his deck.
Like The Fram man says.
Pay me now or....
Pay me later.