Zoysia should grow quite well in your
zone, as long as it is planted in the sun. It actually does well up to 3a, and thrives Up here in Cheese Land, but be careful! Zoysia is a very invasive grass which will choke out just about anything. It spreads like wildfire, and can itself become a unwanted
weed very quickly. In your area, it will be the last grass to green up in the
spring, and the 1st to turn brown in the fall, which will make it stick out like a sore thumb. Once established it is very hard to get rid of, and tends to even be resistant to Round Up.
The best control for
weeds is a good well established turf grass, but unfortunately the same stuff that the turf grass likes is also what the
weeds tend to thrive on. Your best bet is to use an over the top broad leaf
weed killer during the
spring and early summer, and re
seed the area in the early fall. By seeding then the
weeds will not have a chance to over take the lawn.