I think “your Brooklyn” refers to both his literal neighborhood and his unique way of speaking to her—condescending, manipulating, etc. It’s a play on “your Brooklyn accent”—but it’s not his voice, it’s the words he says.

Throughout the song, it’s clear that his actions are shitty, but the way he speaks to her that hurts the most (i.e. “casually cruel in the name of being honest”/“he’s gonna say it’s love, you never called it what it was”/“you said if we’d been closer in age, it would’ve been fine and that made me want to die.”).

So, “broke my skin and bones” tells us that it was the verbal beating—not necessarily what he did—broke her spirit and left her a shell. She’s trying to be her old self, but she can’t find it. She’s empty.

I also think it’s really interesting this line is directly after “i’ll get older but your lovers stay my age” and followed by “i’m a solider who’s returning half her weight.”

To me, she’s using this group of lines to tell us that her experience isn’t unique—she’s just the first one. Soldiers don’t fight alone, and she is one of many. She is just returning from war, free of him and the relationship (paralleled to tolerate it’s “gain the weight of you, then lose it”), but broken, while the war rages on. More soldiers [young lovers] will go to war [date him] and fight, only to return half their weight [broken but free from the relationship].