Lower weight zoom option?
Adding in a curveball which I am enjoying in Turkey now: The Sigma 18-50mm f2.8 on a Sony A6xxx
X100V 478g (great for street but too limiting for travel imho)
X-T4 607g + 16-80mm 440g = ~1050g (heavy but good range and stabilization)
Oly 414g +12-40mm II 382g = ~800g
Sony A6000 344g + Sigma 18-50mm f2.8 290g = ~650g (great weight, but more limited zoom range).
I had trouble finding a newer Sony, so you should round the weight up a bit in case you find something better. Newer ones are heavier but the A6100 may be a similar weight. I would guess plus 50g a6400 or 100g a6600.
As I am traveling in Turkey I am not missing the Fujifilm sims i.e. I want natural. The Sony Sigma combo is a weight I can live with all day and the lens doesn't have the mixed reviews the 16-80mm gets. I haven't once wished it had stabilization but you may find a newer Sony body with it. In the Philippines only the A6000 was easy to find new or used. I like the body and don't miss Fuji's controls like I expected I would. I took my Fujifilm XE2 with pancake out just once. It was a nicer weight but limiting for travel: You surely don't want to be cropping all the time.
A bonus of having such a cheap body (and the lens is very affordable), is that I am happy to bash it a bit e.g. no bag and letting it scrape on rocks after climbing an ancient amphitheater. If you compared the prices as well as weight, then it would show a similarly rosy picture for the Sony Sigma combo. AF is definitely fast enough, 24MP is plenty. It's a baragin, but I will be looking for an A6400 (or A6100) when home for the "super focusing". Lens has very near close focusing, which is a big plus as there are loads of nice cats and dogs on the street in Turkey.
Popping the XS10 in there, which weighs 465g, bringing the combo down to ~900g.
I guess it will depend if you will appreciate an f2.8 too. From what people have said I assume the Sigma is superior optically on average, as all copies seem to be good, whereas the 16-80mm has people talking about smearing and other issues sometimes. One minor negative of the Sigma is that the Lightroom profile doesn't fully fix distortion. Without the profile it is like a fisheye.