I have the Arkel Big Bar Bag, and I really like it.

When my wife and I were doing day tours on a older borrowed tandem, where we couldn't easily add racks, we were able to carry everything we needed for the day for the both of us between a purse carried messenger bag style, and this bag. It has plenty of space for a small picnic lunch for two, or for restaurant left overs, along with a wallet, light jacket, point-and-shoot camera, etc.

I'm not a particularly weight conscious cyclist, so I don't particularly notice nor care about the unloaded weight of the bag, and even when fully loaded, it doesn't have much impact on my steering.

The Arkels have the best handle bar bag mounting system I've ever used: easy to put on and take off, and no wobbles.