Slender aster with flowers, Choess, Wikipedia.org
Slender aster is a common weed that's found in the Southeast and appears in late spring as the temperatures get warmer. It can grow to be about 3 feet tall and produces violet or purple flowers that form seeds, which are easily dispersed in the wind. If you want to kill slender aster, it's important to perform regular lawn maintenance and to take preventative action before summer.
Because slender aster hides in other tall grasses and weeds, it's a good idea to keep the lawn mowed to a short height, at least 3 or 4 inches tall. This weed also germinates in late spring and early summer, so you'll want to apply a pre-emergent herbicide in early spring before it grows and produces flowers and seeds.