Thanks for your question to Ask Extension--good photo! However, it's sometimes difficult (and risky) to ID a plant based on only the leaves and without the blooms and seed structure (does it flower on a long stalk, e.g.). It is also helpful to know the size of the plant in question and the growing conditions (lawn, flower bed, woodland, field, etc.), wet area? shady? etc. That said, I think we will want to continue this dialogue.

It seems from the photo that the stems and leaves radiate from a central point (please check this and if not, send a reply) which is called a rosette. Several thistles and cresses have this characteristic, though thistles tend to have jagged leaf edges whereas the cresses tend to be smooth. I've looked at the leaf images for: pursalane, sow thistle, nipplewort, water cress, knot weed, knapweed, KY glade cress and several others. The cresses seem to be the best possibilities for your plant; some cresses are edible (don't go there yet!) others are not and can be difficult to eliminate. Water cress needs a wet, muddy environment.  Winter cress (Barbarea vulgaris) is bitter (see: http://commonsensehome.com/winter-cress/); and http://www.luontoportti.com/suomi/en/kukkakasvit/wintercress; and

bitter cress has leaves very similar to winter cress and produces white flowers whose seeds "pop out" or "shoot out" for dispersal as the plant matures. See http://the3foragers.blogspot.com/2012/03/hairy-bittercress.html and http://identifythatplant.com/hairy-bittercress-cardamine-hirsuta/ to compare with your plant. We may very well have to wait until a flower is produced to assist in a complete identification.

So where does that leave us? Please check the above links and if you feel that a cress (or thistle) is not correct, send a reply with more info from the first paragraph...and anything else you think might be pertinent.

Regarding weeds, the general thought is a weed is an unwanted plant in competition with a wanted (cultivated) one...and some add that the weed is capable of taking over (e.g. kudzu, johnson grass and winter creeper) by outcompeting the native or cultivated plant. In that light some thistles as well as bitter cress are weeds. So we want to get the ID right!  The following site gives KY state-listed noxious weeds:

http://plants.usda.gov/java/noxious?rptType=State&statefips=21

Oh! If you think that bitter cress is correct and you want to eliminate it without chemicals, a quick and heavy mulching of 3-4 inches before the seeds mature will control next year's plants and minimize spreading; it may take a couple of seasons to be completely effective; a pre-emergent application might also work and take a couple of seasons (e.g. for lawn treatment); pre-emergent s act on all seeds....

I hope this helps! Please continue this query if you have questions or wish clarification. It will be interesting to know what the flowers look like!