Lacey,
You may be happier with your Zoysia grass if you can convince your landscape maintenance guys not to cut it super short. 2-1/2" is a pretty good height to keep for most of the year. Cutting it once a week often takes off too much, especially if the growth is not active.
Often, I would have them edge weekly, but cut every other week.
Cut too short, it becomes stressed and bare ground is ripe for weeds to settle in.
Left a bit longer, it gets thick, and weed seeds do not find a place to nestle in.
I like the Southern Living (magazine) website. One of their writing staff is Steve Bender- aka The Grumpy Gardener. Take a peek, if you're interested and search for his article on Zoysia grass. I love this guy!
The only downside to Zoysia, in my opinion, is that it turns wheat-colored in winter dormancy. Otherwise, it can be quite a beautiful turf grass.
