According to https://forum.freeadvice.com/neighbors-boundaries-108/waterfront-right-way-dock-536952.html
(helpful suggestion of site), how far the dock is from your property is an issue.
So, in that thread, one poster (#3) alleges that in NH a dock cannot be closer than 20 ft to any neighboring property in any direction without a signed waiver from that neighbor, and that in order to the NH state DES issues the dock permits. How close is this dock? Did you sign a waiver? Did your neighbor have the appropriate permit from the DES (plus whatever extra requirements your municipality has)?
This of course assumes that your property has waterfront rights in the first place. Yes, you can have waterfront property without waterfront rights. I have a neighbor who has waterfront property with no docking rights, as part of the deed, when they purchased the property from a marina; they have property with a riverfront, the marina has built an extensive maze of docks completely across their riverfront.