Hi, Elsa, welcome to Permies!
I have some sympathy with your concerns because I am dealing with a lot of giant ragweed and
honey locust (somewhat similar to your black locust) on the 40 acres we live on. Except our honey locusts range from seedlings to 40-foot
trees.
My first question involves your long-term planning for the land. Unless you are pretty sure you don't want to make a productive forest (food forest or woodlot or windbreak or wild animal habitat) on any part of it, I'd hesitate to mow the black locust seedlings. For one thing, most of them will come back in the spring anyway, unless you're planning to spray toxic gick on them which I assume you aren't. But they will be set back. And no matter what kind of forest you want, having some trees already there will make establishing new trees much faster and easier. Many people like having black locust on their land; they're more controversial as a forage/fodder crop than honey locust, but all agree they are the most energy-dense
firewood out there.
Regarding the ragweed, I got nothin'. I defend my growing spaces by hand weeding when they are still less than 24" tall; once they are huge, they win for the season. My weeds seem to move around and favor different ones depending on the rain patterns; year before last it was all horse
nettle, last year it was giant ragweed paradise, this year it's something that grows about seven feet tall that I haven't identified, possibly some kind of broomweed.
Good luck!