I'm sure different parts of the world have different weeds.
For me, the worst are:
Variegated - someone planted it there, then it decided to take over the earth.
Nonvariegated - probably reverted from variegated, and even more aggressive.
Bishopweed, also called Goutweed (Aegopodium podagraria); It's sold as an ornamental. It has brittle underground stems, so when you pull it up, it leaves multiple nodes to sprout underground. I''ve been trying to clear it out for 9 years, and it just keeps spreading. This is the most frustrating invasive in my yard.
Canadian Thistle: Not really that invasive, but it's painful to pull out, so I put it off, Then they grow too big.
Himalayan Blackberry: Around here, it's like kudzu with attitude!. Seems like you've got it all pulld out, then the next week you ahve 6 ft, very thorny stems. Ouch ouch damn damn. The up side is that if you miss it until it bears fruit, they are SO good!
English Ivy: Even roundup doesn't kill it. Not that I use roundup, but I tried a few years ago. It just made the leaves shinier.
Apparently, you can eat Bishopweed in salads. I just pull it out and feed it to the chickens, they love it almost as much as they love dandelions. That makes it less like doing a hated chore, pulling out weeds, and more like foraging.
We also have weeds that I don't know the names for. One that I learned is StickyWeed (Galium aparine). I had no idea what it was called. It isn't as invasive as some of the others, and the succulent stems and leaves are another treat for the chickens. The leaves and stems have tiny velcro-like surfaces and stick to clothes and each other. I did a search on it, thinking this is a sticky weed, and it turns out that the common name is stick weed.
I think one might be Gallant Soldier (Galinsoga parviflora) - it looks like this. It's extremely prolific, comes on with compost, but is relatively easy to pull up. Another chicken favorite (There is a trend here)
Interestingly, a lot of weeds are apparently edible. I haven't tried them. Dandelions, lambsquarters, and according to some web sites, bishopweed and stickyweed.
We also have some weeds that I don't mind, like dandelions (a chicken favorite). Also, semi-invasives like parsley and cilantro, that I let go to seed and now come up all over the place. Which we then eat. And some that I should mind, but dont, like mints. They are invasive, but I like the smell when I pull them up. The chickens dont eat the mint. They don't eat lemon balm either, but I like to pull it out and spread in on the grass before mowing. Smells very nice.
Side note: google search on weeds turns up a lot of info on marijuana. Strange thing is, people aren't trying to eradicate it, they are trying to grow it. Imagine that! No idea whether chickens will like it.
The bishopweed seems to be getting ahead of me again. Im using an organic weed killer, "Worry Free" that I think is made from a citrus extract. Vinegar would be cheaper. I should try it. The "Worry Free" does seem to be weakening the bishop weed in the areas where I have tried it, but it's in a lot of areas. It also seems to work on lemon balm, which is highly invasive in my yard. I think I am definitely almost rid of the Canadian thistle now, using the same product.
This time of year seems very important in weed management. They are growing like crazy now.
Another home remedy for your weeds. Plain old salt water - it really works!