On a passenger vehicle what is carried in the car reduces what can be towed. The standards "tow rating" provide for full fuel and an allowance (usually 150 pounds) for weight of driver. Thus you may be looking at something more like 1000 pounds or less for the trailer weight.
Having been looking for lightweight towable RVs two years now (I've had a target of about 2200 pounds) I suspect you are not going to find anything with a bathroom and shower. Since your tow capacity is likely also qualified with a "maximum frontal area" you will be looking at folding tent trailers, or possibly A-Frame hard-side folders.
You can find very small folding tent trailers with empty weights around or under 800 pounds, but these are in the "tent up off the ground" category. Cold-water pop-ups in an 8-foot box, about 1200-1500 pounds empty. Hot-water plumbing usually starts in a 10-foot box, 1800-2200 pounds empty. Pop-up with cassette toilet/shower unit is usually a 12-foot box, often a slideout to make room for that bathroom, about 2400-2600 pounds empty when equipped for the bath (brochure specs are usually without the bath).
Hard-side folder, 12-foot box, with toilet/shower will be 1800-2000 pounds empty, but in that box size with a toilet your dinette will also be your sleeping space. Advantage of pop-ups is that the beds get pulled outside the box, hard side A-frames all the living space has to fit in the box.
Egg-trailers, small molded fiberglass units like Scamp and Casita, when equipped with a bathroom, come in at a little under 2000 pounds at 12-13 foot, around 2500-2800 in 16-17 foot models. They are somewhat lighter without the bathroom (space gets used as seating/bunks or for storage). In a 12-13 footer, your dinette is your bed. In the larger sizes, the dinette is still the main bed, but there are floor plans with a second two-person dinette so you can leave the big one in the bed configuration.
Weights go up from brochure weights when you add options (air conditioning et al). I'm working with my notes from looking at Casita models in the showroom, and Rockwood, Flagstaff, Jayco pop-ups on dealer's lots. Folding tent models, I'm stuck with brochure weights, but you have size choices all the way from motorcycle tent trailers up to 12-foot boxes, they just fold instead of pop-up.
Reality is, except for folding tent trailers, the target tow vehicle for small, lightweight RVs in the U.S. market is the mini-van or small but powerful SUV rated to tow 3500-4500 pounds. Sub-compact and compact cars, compact-size four-cylinder SUVs, the RV you can tow will be something designed for the motorcycle camping market. That gets your tent up off the ground, and usually with the bed(s) folding out on the front or side, it means you get from the bed to the floor in a sitting position. For some of us growing older tent campers, that can be enough, but it is not really a transition to RV camping.
What do I think of it, not owning but looking? I've looked at several options.
I really like the 17-foot Casita. I think I could be OK in it for weeks at a time, alone, but with one other person the confined space would drive two of us crazy in a short time. I have a friend who has used this one for ten years now, he loves it, but his late wife did not RV with him, he used it alone. I would need a better tow vehicle than my Ranger truck, no way I an going to tow it with my sub-compact car.
I've looked at A-frame hard siders, like them also. One would work for most of the "camping" I do, but the limited space means I have to choose between having a bed and having a toilet (shower not an option). There are some larger hard-side folders, but they get too big for my tow vehicle. I could do something about that.
Pop-ups, disregarding the weight issues, I could have my living space, sleeping space, and a minimalist occasional use bathroom. More sleeping space than I need, but my kids could use it. However, I come to this one with some pop-up experience. Setup, breakdown is more work than my tent camping has ever been, I've been pretty minimalist on that, a few things in the trunk rather than 2-3 truckloads of camping equipment. The real issue is that I don't want to be in a PUP during a midwest thunderstorm, and I wouldn't be using it when the camping season gets into either 100 F days or sub-freezing nights. Thus I would be keeping the motorhome and using it for most of my outings. But coming from a tent, you might like a PUP. You just need a bigger car to tow it.
One more alternative,
Camplite trailers are probably about the lightest for the size, even the smallest has a bathroom of sorts. But it is also too heavy for your tow vehicle.
