It's hard to see the individual weeds, so I can't tell what you've got. Can you just pull them up? Maybe with the help of a pitchfork or spade? You could also try a layer of newspaper or cardboard with mulch over it.

Can you just cut them down with a weed whacker? Before they flower they'll be an ideal addition to that compost bin. They are just doing what comes naturally ie trying to reproduce. You won't be able to keep them at some sort of ideal height without constant attention. Are you averse to clearing them and mulching? Clearing them and extending the lawn? Clearing them and planting shrubs/perennials? I'm not really clear as to what your plan is for that area.

All the time there is nothing else growing there weeds will come.

This post was edited by florauk on Mon, Aug 19, 13 at 4:42

"Weeds" are simply plants you do not want growing where you do not want them growing. If you keep them mown they will be less visible, but keep in mind that many of what we call "weeds" are food and shelter for many of the beneficial insects we also depend on.

I'm not sure I understand your goals, and whether your focus is on appearance or utility? You want a kind of 'wild garden' that you occasionally trim? Are you going to add plants on purpose, or just work with what shows up?

Generally, I would try to eliminate exotic plants and encourage natives that are an appropriate size for such a garden, then not worry about trimming anything. There are many native plants that traditionally colonize at the edge of woody areas, although this may be in full sun if the trees are to the north of this area. A barrier/border between wild area and lawn would probably be helpful in maintaining control (and with appearance, but that's just my opinion.)

Thanks all for your responses.
I guess I didn't explain fully what I was looking to do. But it was also a question for the more experienced. If I kept the weeds, would there be any harm to doing that as I like the natural woodsy look. I know they will spread to a point. I do realize if I cut them down that I could have lots of greens for the compost bins. If I cut them down to the ground I can pull as much of the root out as possible would i have to put mulch down every year to keep them from coming back or could I get away with a few years before refreshing the mulch. I guess I'm looking for more opinions on what to do for both ends (cutting them down or leaving them but trimming for an attractive look)
I will take some close up pictures later in the day.

There is no 'harm' in keeping the 'weeds' if that is what you want to do. You are mowing the lawn so they won't colonise that. But you also have a vegetable garden there and they WILL get into that.

The kinds of 'weeds' which colonize freshly cleared ground are the opportunists, mostly annuals or coarse perennials, some of which will be non natives. If you can take some close ups we can tell you what you have there in more detail. I think I see a good deal of Sonchus aka Sow thistle.

If you want a 'natural' woodsy look, I would suggest you clear out the fast growing annual weeds (which is what you appear to have) and look into more choice natives. You could have a great mix of low shrubs, perennials and ephemerals suited to your area.