Answer: Balsam pear is an annual plant so removing all the vines will take care of the current problem. What you find sprouting are seeds that spilled on the ground from the fruits of the original plants. Pulling these sprouts out as soon as you recognize them is a good first step. You might also consider applying a pre emergent herbicide in areas where you do not plan to plant seeds of any kind. Pre emergents will stop weed seeds from germinating. There are several brands on the market, many of them corn gluten meal based, so read the labels and use the product that is labeled for use in the area you wish to use it. (For instance Preen can be used around woody ornamentals and there's also a formulation for use in vegetable beds.)
Best wishes with your project!
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