I was going to say the DVA bars mentioned above are the thinnest I’ve seen too, if you need them on all the time. I’ve bought other products from them and they are great. The downside of these rails is the weight limit of 100lbs (I think that’s per bar, but not 100% sure)
Personally…I like my own setup. I have 2 bars from Leitner, which add about 3 inches to the height. They replace the factory bracket on any of the 6 brackets on each side, so the downside there is you’re more limited in where you mount. The big reason I like the Leitner bars is I can loosen 4 13mm nuts on the t-bolts connecting the bars to the brackets and then with my fiancé lift the 2 bars up and off with anything mounted to them and keep the setup in the garage when not needed while the 4 bracket replacements stay on the car permentently and easily go unnoticed. We do have to empty the toolbox and water tank before we lift it on or off.
I also like how the bars have t-slots in all 4 sides.
There’s a closeup of my Leitner roof rails and DVA Jerry can mount.