I can tell you my experience.
I have an 05 GX with 200k miles and a 2" inch lift with 285/70 17 tires (10 ply rated). I started with a 3800 lb (dry) airstream which I took about 4-5000 miles through the northwest, BC and Alberta. Overall, I think I got around 11-12 MPG. With a properly set up weight distributing hitch, adjusted trailer brakes, clip on tow mirrors and tires at 55 PSI. it was just fine. It was my first experience towing and only felt uncomfortable when there were high cross-winds or a semi passed at high speed in the opposite direction on a 2 lane road. It was never hard to control and I had no sway or porpoising.
We sold the 22' bambi a few years ago and now have a 23' CB (looks like what you have). I do notice the larger weight and size when accelerating or in headwinds but, again with a proper WD hitch and adjusted brakes, it tows just fine. Get comfortable with 3000-3500 RPMs. My MPG going through Utah on I-15 is 10-11. With the bigger trailer, I have added a larger transmission cooler and in the summer it has crept up above 200 degrees but still have gone over 10,000' in the Uintahs without a problem. Certainly, this car was not made with the intention to tow on a regular basis (it says so in the manual) but it really can do it as long as you keep everything within spec. Dry weight is almost meaningless. Get your trailer set up for a typical trip with all the water, propane and crap that you will take with you and then weight it. Go to CAT scales near you or take it to an RV shop and have them weight it. Be sure to double or triple check your WD hitch set up and don't just trust some schmuck at the RV shop to do it. I've seen some very scary set ups. Keep transmission in 3 or 4 to keep RPMs up and ATF circulating.
The most troubling part of that trailer is the heavy tongue weight with two large LP tanks and the two lead batteries so far ahead of the axles and then all the gear people carry up front. I usually only keep one LP tank full (may consider going down to 20 lb tanks instead) and fill the water tank at or near my destination. I also tossed the 100 lbs of deep cycle batteries and converted to lithium (30 lbs) which I keep under the couch closer to the front trailer axle to move weight from the tongue.
Be sure to avoid exceeding payload of the GX as well once you add passengers and gear inside on top of the tongue weight.
I love being able to actually go on trails once we get to our destination and for this reason alone have avoided buying anything full-size like a pickup or sequoia.
I have towed this same trailer with my father-in-law's Duramax Silverado from northern Utah to Bryce to compare it to the GX. In the diesel, we got 12.5 MPG at 75 MPH overall compared to 10.5 MPG at 70 MPH in the GX. GX is so much more comfortable since the engine is so smooth even at the higher RPMs. I am extremely defensive and alert when towing, keeping plenty of distance between myself and the car ahead, avoid sitting in a blind spot and watching for erratic or aggressive drivers or brake lights far up ahead. I'm sure if I weren't paying attention and had to make evasive movements on the highway, a large truck would be safer.