Weeds have a magnificent way of surviving no matter what we do to them. I think purslane (Portulaca oleracea) would survive a nuclear blast. Common lambsquarters (Chenopodium album) loves rich soil so much that it doesn't need an invitation to sprout in every new flower bed and vegetable patch I prepare. Yarrow (Achillea millefolium), a common perennial weed, with its underground creeping stems doesn't care in the least about what it's creeping up on. Let Canadian thistle (Cirsium arvense) get established and you might have to dig 20 feet down to find its taproot. What will you dig that out with, eh?
It's all a part of growing stuff isn't it? You could stop gardening altogether and let the weeds take over. I have three hosta beds that I've neglected all summer, I had plans of transplanting everything to a new home, but then I'd just have to worry about weeding that area too. It seems to me that when left to their own accord, both weeds and what we grow as ornamentals get along together just fine. We're the ones who don't like their living arrangements.
Johnsongrass (Sorghum halepense) is considered an invasive weed in Pennsylvania. This particular clump is managed as ornamental grass in my wife's herb garden.
This strand of bindweed is havin a lot of fun vining up a large clump of zebra grass. I haven't noticed any bud formation so I'm not sure if it's wild morning glory, or some other member of the flowering convolvulus family. Weed lady and author Nancy Gift ("A Weed By Any Other Name") allows this perennial vine to climb on its own personal trellis.