This is classic MYOG.
You see, what you are looking for has too little value-add for most gear vendors. They can't sell something like this for less than maybe $50 (I dunno), but who is going to pay that much for a simple stuff sack? (Well, not me, anyhow!)
I have some 10" x 16" MYOG stuff sacks (PU-coated nylon, maybe 60 gsm) we use as food bags in the tent in the evening. One bag holds all the lunch stuff in the evening, out of the way, and the other holds all the dinner stuff. OK, hardly SUL, but very very convenient.
I have added short loops of 5 mm tape to the two bottom corners. Then I take a few feet of 5 mm soft light webbing and tie the ends to these two loops. Fill stuff sack with day gear and tie the middle of the 5 mm tape around the neck. Onto the shoulders and away we go. Perfect for short side trips during a thru-hike.
Total weight: 46 g (1.62 oz). Short of making it out of Cuban, I defy anyone to make anything much lighter.
One version is deluxe. I reinforced a bit of the bag near the top and added another short loop of 5 mm webbing. I tie the middle of the 'shoulder straps' to this instead with the length adjusted to suit my shoulders. Now I can open the 'day pack' by undoing the draw cord at the top without undoing the shoulder straps - so they stay the right length.
No photos right now - camera being repaired.