Over time, the less tilling you do, the less new weed seeds will make it to the surface.
In the early spring, I let the first crop of weeds sprout then use my scuffle hoe to cut them down by scratching up the first half inch of soil. There should be very few unsprouted weed seeds left in that layer when I plant my vegetable seeds so weeding isn't as overwhelming as that first bloom of weeds can be. By letting the weeds sprout before planting my crop I can just scrape them all down without worrying that I'm killing the plants that I want.
No matter how you started out, as your season progresses and your plants get bigger, there will be less weeding so hang in there.

Mulching is great too. I use straw if I can get it or leaves. As I weed, the weeds (unless they've gone to seed) get added to the mulch layer.