I haven't been able to crack 6oz for an insulated mug with a lid. I found some old Rubbermaid ones that are about as good as it gets and the capacity is nothing to brag about. You can get 12oz or better travel mugs with lids, but they weigh about 12oz. too!
I think a lid makes a bigger difference for the weight than the side insulation does. I use a GSI plastic mug that is 2.5oz and it could use a lid --- keeps the bugs and fir needles out of your coffee too.
Years ago Hoagies had a promotional coffee cup that was perfect for camping-- about 8oz. capacity, light, and had a snap on lid. You got one free with a cup of coffee, which made them even better :) It was just a simple single-wall mug with a lid.
I dug around in my gear box and found the insulated mug-- it was made by Thermos, not Rubbermaid, and by golly, it holds 12 ounces and weighs 4.3oz with the lid.
So I went surfing to find an example and I think we're out of fashion. All the insulated mugs made now are some stainless steel Starbucks knock-offs. I found examples of the Hogies mug on Ebay, but they are all odd-ball collector promotional items for oil companies and such and going for $10 + frieght.
Somewhere in the depths of K-Mart or Wally World, there must be a plastic mug. The search for the trail grail continues.....