You might try a thick layer of straw between the rows to shade out weeds. In my experience, the few that do grow through pull out easily. The only downside is that if you get slugs, the straw will make the slugs worse. I used to put out a couple of old beer bottles on their sides with top at ground level, with a little beer or yeast and sugar water, and the slugs crawled into the "hotels". There is always weed control fabric, or plastic sheeting. but I have never really liked using it in vegetable gardens.
@jyoutz FWIW: we used something similar as a kid, but we used either hemp or sisal twine so at the end of the season, it could all be turned under for compost. I could see that it might depend on the local climate.
All the best,
Peter