Sometimes you need to know the exact weed before you can kill it. In this case, whatever it is, it should be treatable with a broadleaf weed killer like Ortho Weed-B-Gone. WBG will leave your grass alone and only kill the broadleaf plants. Watch your overspray because most of the plants in your yard are broadleaf. You only need to mist the leaves of the weeds. WBG is not a soil drench. Some weeds take a little time to die. The Weed-B-Gone works by hyperactivating the growth hormone in the plant. It dies by exhausting it's energy reserves. So it will look healthy for several days...and then it's dead. Unfortunately it is too late to seed for this year in your area. Once the weeds are gone, you will be left with bare soil which will attract more weeds. This is especially true if you seed in the spring. You might try dormant seeding to help 'densify' the turf. With dormant seeding you seed in the winter hoping that the seed will sprout early before the weed seeds are sprouting.

They look like hackberry seedlings to me. The blog post I've linked has an excellent clickable picture of a hackberry seedling, it's the 9th picture down. Here is a link that might be useful: The Birth of Trees

I see faint, dark blotches in the middle of the leaves, so it's one of the lady's thumbs (which are Pennsylvania smartweed's cousins). Look through all their photos: https://gobotany.newenglandwild.org/species/persicaria/maculosa/ The easiest way to kill it is to pull it before it seeds. This post was edited by missingtheobvious on Fri, Sep 26, 14 at 11:32

Can you tell us what region you live in and what weeds you're finding in your yard?