My dad lived in New England for most of his life. While there, he spent a great deal of time killing crab grass in the yard, over the course of 4 decades of homeownership.
He moved down to Florida to retire. There, he felt that the garden gods were punishing him because every single blade of crab grass he ever killed was growing in his Florida yard, because that is the native grass that grows there!!
We laughed about it all of the time. He called it poetic justice.
So, it depends on where you live whether "grass" is a weed. Regardless, if it grows in the ground, it is a plant, nonetheless.