Not much is known about how this plant reproduces by seed - it is thought that it mainly spreads by growing new tubers - but before we moved in here, this house was vacant for at least two years, so I'm sure a minimal maintenance of the yard provided the opportunity for this weed to spread.
There are several 3-way broadleaf herbicides that can be used for spot treating Florida betony. In addition, lawn weed sprays containing Atrazine will control this weed. I'm not a fan of spraying chemicals on the lawn, but with as much as we have here, it might be necessary. I'll probably spend some warm winter afternoons spot treating weeds in the lawn, but not before I figure out which herbicides to use at: HGIC 2313 Florida Betony