Add lots of mulch between the veggies. So cover the soil with a layer of organic matter and it should smother and inhibit weeds and prevent new seeds from germinating. It's also great for the veggies. You can also mix up a batch of weed killer.
PLace all the ingredients in a spray bottle, give it a good shake and spray the weeds.
Weeds can grow just anywhere and it is always amazing to me how quickly they grow!
I love the vodka herbicide above! I use the vinegar that is sold as a cleaning vinegar in spray bottle w dish soap---super strong. Weeds will grow in the mulch, unfortunately. So I just dig them up---good exercise. Also, you could use newspaper under a walkway.
I have a helpful free resource on my blog that includes 5 tips I use that are really helpful. Beginning with taller raised beds and mulch. The rest can be found on my website by getting my newsletter. It's a free printable.
Companion planting also helps. Veggies with big leaves like squash will crowd out the weeds around corn or other taller plants. Even lettuce can do the same thing.
Years ago I spread a pretty thick layer of newspaper in the paths between rows of plants. It worked for me.