I don't have "weeds" per se, I just have some
volunteer plants that are less useful than others.
Henbit is well naturalized in my garden. Can always count on it to bloom in February and disappear by early summer, only to return when the weather cools off. It never makes a smothering appearance, so it's welcome. So is Carolina geranium. Since the poultry and rodents like to nibble on it, if it starts to get too exuberant, I can always chop it for feed.
Chanca piedra is also well naturalized, maybe a little too much. It's gradually spreading, each year cropping up in new places and thicker in places where it was already established. It's a useful
medicinal herb, so I like to have some growing, but I don't want it choking out other things.
I would like to get dill and cilantro naturalized in my garden. I'm pretty close to it. I don't need to buy seed for these two, there always seems to be a stalk somewhere with plenty of ripe seed on it that I can use to scatter in areas where I want to encourage it. They can pop up anywhere they want, just like weeds, but they are too useful to be called weeds.
Bermuda grass and
bindweed used to be more of a problem, but with the increasing plant diversity, they are having trouble competing. I still pull them when I see them coming up, because I don't want them to become a problem, but it's getting so they are rare enough that I don't have to be very vigilant about it.
Finally, Johnson grass and nightshade are not welcome at all. All nightshade gets pulled whenever and wherever I find it so it can't make berries and set seed. The small amount of Johnson grass is under control mainly because when it gets to a noticeable size, say 2' tall or so, it gets yanked for the guinea pigs. They like the tasty Johnson grass.
Whenever you finish planting an area, Nature takes over and decides what is going to do well, what is going to do poorly, and what companion plants she wants to add. To a limited extent, it is "no big deal". Only when she starts to deviate markedly from your intentions do you really have to roll up the sleeves and get dirty doing some "weeding".