UL mug?

Can not point you to a specific source, but can share what I did.  I received a plastic container as a gift filled with honey, ~12 oz capacity.  I took some thin foam packaging material from an online purchase and made a cozy for the sides and bottom.  The lid fits on snug, did not add insulation here. Weight does not meet your goal of 28g, it is a bit of a pig at 40g.  But it insulates rather well, is easy to clean, does not burn lips and is a lot tougher than a paper cup.  I started at about 110g so not too bad for me.

Yogurt container?

How about Snow Peak Hot Lips?  These won’t keep your beverage any warmer, but they will keep you from burning your lips on your pot.

I think someone on BPL a while back mentioned these InCycle 8 fluid oz cups made from PET as a good insulated backpacking mug.  Inexpensive and light (0.16 oz), they seem like they might be worth a try.

Yes, Yogurt cups. We use Chobani containers for hot chocolate with no problems with burnt lips. YMMV.

My mug of choice for backpacking is a fold-a-cup, which is sold under a few brand names. The one I have was a Coghland’s. Lots of people would probably laugh at it, but it weighs 0.8 oz and folds up super small. The other thing I love about it is that it’s soft sided which makes it great for collecting water from small trickles of water. It also pours really well. The only big downside is that it only holds a cup of liquid. However, that just means you have to fill it more often. I have a pot cozy so if I want more than a cup of hot liquid, I just keep the second helping in my pot.

In summer I usually use an easy mac and cheese microwaveable container cup. http://www.amazon.com/Kraft-Easy-Original-2-05-Ounce-Microwave/dp/B000Q92QIE

It also has a very thin insulating sleeve. No lid though

Use a plastic container and make a little cozy from reflectix. You could even cut off the top of a smart water bottle. The only bummer is no lid. But maybe you could find some thin plastic container with a lid.

What I’ve done is I searched and searched until I found an insulated mug that seems to be lighter than all the others (thrift stores are a good place to look.) I use it to hold my caldera cone and keep it protected and also I shove my little bottle of alcohol in there, so even though it’s not the lightest thing in the world it at least serves a dual use.

Nalgene flask. Ditch the sleeve and the cup and it’s about 1.2 oz iirc. Holds 12 oz, handles boiling liquid, has a lid and fits into a pocket. Add a cozy if you like.

http://store.nalgene.com/category-s/31.htm

+1 on the Easy Mac cup.  Its light, relatively durable, easy to find, and insulates enough.

I use one of those plastic single serving soup cups- I think mine is a Healthy Choice one it had a green plastic lid, I added a piece of aluminum for a lid/ground shield. My cat can stove, lighter, eye dropper of soap, piece of shamwow, and an esbit tablet fit inside and the whole thing fits perfectly inside my titan kettle

I use that same mug as Thomas mentioned. I also recommend it. Solid, will never crack, folks up small, and pretty darn light (less than an ounce).