Some attention to identifying the weed species will help. Firstly, are they perennial, such as couch grass, brambles ,plants that are spreading in from the borders. Are they chance arrivals of wind blown seeds from elsewhere? Deeply rooted docks or dandelions?
Seeds will need to find fine material to establish.Perhaps raking to increase the voids, with the introduction /evening of gravel will help.
Flame treatment would be my choice, you need only to raise the sap temperature towards boiling point to destroy soft plants, not necessary to burn them away, although its quite satisfying to totally blitz the more persistant!
