Pigweed thrives in a bacterial soil. At any given moment, soil has a fungal to bacteria ratio. When it gets reset with chemical or tillage, you lose all your fungal, and you start over again at bacterial dominated. Constant living green is what keeps your fungal alive, and it will build ever higher the longer it's green. Keep it green, and it'll no longer be hospitable to pigweed. This is why it has a tendency to explode when soil is continually reset. Nothing else will grow. All the fungal advantaged plants die because the system changes.
It can take a year or two to advance enough to really snuff the bacterial dominant stuff out, but it will happen because the soil changes. I've been hoping to grow a viable thistle patch, and I cannot keep them alive. I've lost my gold finches because of it. I did get a small canada thistle patch where I was digging last year, but it won't last.