Our barrels are Medium contour. Many folks want a lighter barrel, so they have it turned light weight UHG, which is .625. The lightest is .625 all the way (pencil barrel). We don't due a true "Gov't" because that actually tapers from the chamber to the gas port.
Although in theory, there is more rigidity in the medium or heavy barrels, and should produce better accuracy, we have not had any real world complaints. We have even had some say it got better after a trip to the shop. (maybe it's the magic dust we sprinkle on them).
So, if you want your rifle lighter, then contour. Where you contour is a factor of how light you want, and the look you want. Hope that helps.
Oops- Edit for number correction.