That depends on the "weed". Some will grow back from even a very small piece of root will with many others because the top growth is now gone the roots will die.
Many people, because they have alwasy done it this way, remove "weeds" from their gardens without thinking of the nutrients they are also removing and often those "weeds" bring up other essential nutrients from the soil that many of the plants we like do not, making for a more healthy environment for the plants we like.

Except for the part about about depending on which weed - I don't begin to understand what you just said.

V1 - You might find a garden hand fork useful for those young weeds, looks like a pitch fork but hand sized. You can push it down into the soil next to the weed and loosen soil without turning the soil over - weed and its roots should pull more easily out of your bed. Or, instead of scissors, why don't you pick up something like a dandelion fork, helpful for weeding other than dandelions, a small investment you'll use for years. My own is longer than this one (and almost as old as I am :)):

Here is a link that might be useful:

Yeah, I saw them last week at Target about $6 at the garden section. I was wondering what it was. Now I know. :)

Thanks!

Or even cheaper purchase a long bladed knife from one of you local charity shops.

For years I have used a Old Hickory carving knife on weeds. A quick poke beside the weed, a twist of the handle cutting the weed below surface, and pull. Some with a circle of fiberous roots may need more cuts but be careful. A dull knife is more dangerous than a sharp one because you take more care with the sharp one.