I envision most of the LL cloths as jackets for me as well, save for the Agnelli Tweed, as you mention, and the length of Agnelli Flannel that I have awaiting funding. In fact, I love the Agnelli Tweed so much, I bought a second suit length.
I have only funded two LL cloths so far, a suit in the Agnelli Tweed and a jacket in the City Gunclub 2, but I find both to be among my favorite pieces in my wardrobe. I have no issue wearing them due to the weight. Maybe it is due to my location, but I find them very useful and a pleasure to wear.