I have heard vinegar and dish soap is an effective Canadian thistle killer. Cut the stalk, and pour down the shaft. I don't know what specific species of weeds you have, so don't know how effective it will be on whatever else is there. Not a big fan of Roundup either. the stuff is worse then most of the chemicals we use, for the environment.Once you know what species you are trying to eradicate, do a search for a "green" solution for weed control. Both bases and acids will have some effect in the long term. Perhaps a water spray after the application, will wash whatever your application of herbicide , will reduce the potency of a direct application. Perhaps a soil analysis will determine if the soil is basic, or acidic. If the weeds thrive in this soil, a conditioner in the opposite PH direction may impede the growth. Continuos mowing seems most effective, killing the flowers before it goes to seed. Definitely not my specialty. Only way I have ever reduced noxious weeds on my property, is to pull them before they go to seed. It may take several seasons to do this. Also , you will need to pull in a larger perimeter, so seeds take longer to migrate back.