Yields of most crops - especially onions and carrots - will be reduced if weeds are allowed to interfere with their growth.
Providing deep-rooted and other perennials are dealt with when the vegetable patch is started, the only weeds that should become a problem are annuals and the seedlings of perennials. These are easily dealt with if you hoe regularly. A good sharp Dutch hoe is a deadly weapon if used frequently.
Sometimes weeds will grow in the rows of vegetables in which case a spot of careful hand weeding will be needed. Weeds growing in containers will also have to be dealt with by hand.
Where perennial weeds do become a problem, either dig them up or hand weed, or use a weedkiller based on glyphosate.