Having tried both the Volkl and Babolat leather grips TW sells, I didn't find much difference in their bevel-retaining abilities. They seem to be of about equal weight and thickness, as far as I can tell.
The Volkl feels a little softer -- more pliable -- than the Bab. And of course, if color is a concern, the Volkl is a reddish-brown, while the Bab is a light, almost yellowish tan.
The thinnest overgrip I've run across is the Gamma 2. (Sold here under the "tacky" heading.) I prefer a thicker, plusher overgrip. Bought the Gamma 2 once on a whim, and found it WAAAAY too thin for my liking. I typically use Wilson Pro's, or Yonex Supergraps. So for reference, G2 is at least considerably thinner than those.