The tyre alone is thinner and more flexible than a tyre with a tube behind it. Therefore, the tyre can conform to the shape of the ground giving you more rubber in contact. Therefore, more grip. It's counter intuitive that it can also offer less rolling resistance if there's more grip but because the tyre conforms more, it "blends" with the surface features rather than offering hard edges to them.
I didn't do it for the weight or the reduced punctures, I just did it for the feel. I swap tyres over quite a bit so I got a little compressor. It takes no time at all to reseal a tyre that's been previously used. (However, I tend to stick to UST/LUST tyres now which seal even better on Stans rims)