It's not mine either. (That'd be Down By Law.)
I suspect that viewers' interpretation of Paterson's relationship with Laura, and their perception of Laura, will be very different based on experience.
Some find Laura too MPDG-ish. I've met, and call as close friends, several women who remind me of Laure, and they're not behaving like her to get guys' attention or to be liked. They are irrepressibly creative, and constantly throwing themselves with enthusiasm into new kinds of creative pursuits.
To the issue of codependency — I don't see it. Paterson seems capable of taking care of himself. He was a Marine, and he still follows some of the rigors of those routines. He is watchful and careful in caring for the passengers on his bus. He listens to, enjoys, and takes action to protect people in the bar. He doesn't need a housekeeper (although he might need a cook). I think he's with Laure because it delights him to support her creativity.
And lest we make too much of her "sitting at his feet," hoo, boy. We might remember where she's likely to have come from, and the typical body language and gender-role norms in that culture. We might remember that some couples might interact this way without seeing any of it as hierarchical — it might just be humility and tenderness.
Is their relationship perfect? Of course not. It's not hard to imagine what issues they would bring up if they were seeing a therapist. But that's part of why they seem very human to me.
I almost always agree with Darren Hughes. But "desperately clinging to beauty in the mundane"? I recognized Paterson more than almost any character I've seen in the movies. He is distracted by, delighted by, beauty in the mundane. And let us remember that, like Alvin in The Straight Story, he has suffered some kind of trauma at war. His response to the near-violence in the bar shows us that. He's walking wounded. I imagine he feels gratitude for even slight experiences of grace.
Also, for what it's worth, these poem were written by an accomplished poet to represent the work of an amateur poet. Paterson's poems remind me of poetry by some of my favorite poets, even if they don't remind me of those poets' best poems. They sound like poems by undergraduate poetry students who would make me think "They get it. They're beginners, but they get it."
For whatever it's worth: My wife is a published poet who has taught poetry and received endorsements from some of our favorite published and accomplished poets. She likes Paterson. She enjoys his poems too. They're not T.S. Eliot, but they're more complicated than they might seem at first. They demonstrate an awareness of all kinds of "play" between words, their sounds, their meanings, and their possibilities.
Paterson is not supposed to be a genius or a great poet. He's supposed to be like the rapper in the laundromat — a guy who, despite the ordinariness of his life, is alive because he is awake to some form of play, and that lets meaning into the incidental. It would seem arrogant and hard-hearted to me to scorn such characters as "not real poets" because they're "not good enough." That would be like condemning James Taylor because Radiohead, or Billy Collins because W.H. Auden.
Having said all of this, I do think there is a certain messiness missing in Paterson that I love in other Jarmusch films. There's a "grit" in Down By Law — and even in Only Lovers Left Alive — that I miss here. But they all have a great deal in common — particularly a love of language, of the power of play, and of strangers who speak different languages connecting over a shared love of particularity.