I've resorted to chemicals. I weed each bed just once a year, then I apply Dimension or Preen. This year, with growth starting so early, I'll either have to apply the Preen twice, or buy Snapshot, which is more expensive, but lasts a lot longer.
I will never ever again use weed fabric. I've had a lot of people pay me good money to remove fabric that they had installed by others. Our bermuda grass loves the weed fabric. It gets good and established under it where you don't see it, and then once it's strong enough, it breaks through and you basically have to dig out 3 feet of dirt to get all the roots out. The thorny roots weave through the fabric where, to take out the fabric, you have to dig out the roots that are holding it.
Dirt blows in (from Colorado, thank you) and covers the fabric and weeds take root on top of it. There's a whole page full of reasons I won't use that stuff....and a few on why I don't like using the chemicals either, but I tried going completely organic and ended up with surgery on my hands and knees. Doc said i could either give up gardening, or pay someone to weed, or pay for more surgeries or garden using weed killers. Preen is my friend.