I think I've identified it - This appears to be ragweed and the source of my near-constant sneezing. 

Is there a good way to control it in the fall? Will mowing help, or will that make it grow back stronger? 

Ragweed plants like to grow in heavy, untilled soil and are frequently found in soil that is uncrowded and has poor fertility. They also do not tolerate being mowed very well. Due to this, one of the best ways to control ragweed in your pasture is to make sure it is mowed regularly.

Herbicides are a common way how to kill ragweed. Ragweed is considered a broadleaf weed, so you can use broadleaf weed killers on it to help get rid of it. In recent years, however, some varieties of ragweed have started to build up a resistance to these common weed killers, so using herbicides may not be 100% effective. If you decide to use herbicides to kill ragweed, the best time to apply them is mid spring to early summer. Controlling ragweed at this time will assure that you are applying the herbicide when the leaves of the plant are still rather immature and tender and, therefore, more susceptible to herbicides



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