In order to do battle with anything you are far better off to know your adversary and then take counter-measures. In this case, I would find out what the plant is, and then find out what it thrives in. Weeds are natures way of letting you know a nutrient imbalance is taking place. Once you know what your soil is lacking, or what you have an abundance of, you can figure out a way to change it.
For instance here we have lots of problems with golden rod taking over pastures or hay fields.The best way to deal with it is to actually spread urea on the pasture. This ups the nitrogen and makes the grass compete with the golden rod...so much that in a years time the golden rod is on the retreat. In the meantime we get better grass that keeps the milk production up.
Lime also may help depending on the weed in question is nitrogen loving or alkali loving. Lime and Urea are both easy broadcast spread over a pasture so its a no invasive way of dealing with the problem (no tilling or spraying herbicide).
I have no intention of traveling from birth to the grave in a manicured and well preserved body; but rather I will skid in sideways, totally beat up, completely worn out, utterly exhausted and jump off my tractor and loudly yell, "Wow, this is what it took to feed a nation!"