To weed nut sedge you must dig under sections and pull out the whole root structure. You cannot just pull out each weed individually because as you can see they are actually connected together. It is best to weed methodically starting at one end and working your way down.
Nut sedge growing between beds Nuts sedge root system
The nut sedge root system is called a rhizome. Nut sedge does not grow from seeds but instead spreads via its root system.
Want even more information on weeding? Then check out: "Managing Weed Overwhelm: A Practical Organic Approach for Real Results, with Margaret Roach-Encore Presentation"