Hi
Hope you get some good answers. I rely on getting down on the ground and picking them out one at a time lol Don't recommend that at all.
Most troublesome are ferns ,particularly nephrolepis.
Maybe it would help to know what kind or weed?? gary

The weeds vary - most are a broadleaf type. Would Roundup kill the moss as well if I used it?

I had heard that Roundup (glyphosate) wouldn't hurt moss and my moss yard was badly infested with grass and broadleaf weeds. So last fall I sprayed it with glyphosate and it sure did kill the weeds and grass but it also killed the moss. Since then I've learned that SOME mosses will withstand the herbicide and some won't. So if you want to try, test a small patch and see what happens. Give it several weeks before spraying the whole area. If it hurts the moss, then you can paint the individual clumps of grass and weeds with a sponge type paint brush dipped in Roundup. Be sure it doesn't drip onto the moss. More time consuming than spraying but much easier than hands-and-knees pulling.