This is all to do with the way Roundup gets to work on weeds. The weed may look healthy still on the outside, but rest assured the plant is dying on the inside. Roundup’s systemic action sees the weed killer moving down through the plant to kill the roots. Usually, within two weeks, the leaf tips will start to wilt and turn brown. Roundup works faster when weeds are actively growing. If weeds are not growing vigourously (e.g. in cold weather, or if the plant is stressed by drought), the process may take up to 4 weeks.