I have the size small kelly kettle. I'll have to weight it again but if I recall it weighs something like 16 or 17 oz.
1. I think 12 oz or even less for an ultralight version would not be that difficult. The size small kettle is listed as being a pint, but I think that refers to an imperial pint as the actual capacity is something like 24 oz. So just reducing the size, say down to 12-16 oz without changing anything else would reduce the weight. There are a few other things, like the bail I think is steel, and the kettle uses a wood handle, so these items can be lightened. I think it would not be too difficult to have something down in the 8-10 oz range.
2. As for using one of these under a tarp, I would not do it, as the flames (and embers) tend to shoot out the chimney, especially when you are getting the fire going or adding twigs to the fire (This is with the kettle on the base). It's pretty impressive, the flames can shoot out a foot or more above the kettle, which is already tall to begin with.