Pestly plant invade my vegetable garden

This plant invades my vegetable garden every year. It's the only plant that seems to love thriving among my vegetables and it's almost impossible to wipe this plant off of my veggies. What's the name of this plant and how do I get rid of it. I pull them out by the roots but they send out runners and the multiply very rapidly. Hellp............Please if you can.


Thanks

 

Looks like chickweed.

 

Sure does, and if that's the case you'll probably never be rid of it by simply pulling it up. Most people resort to chemicals, but if it's your veggie garden I'd just learn to tolerate it. It's good in salads!