Rob, although the 18-135 is a cracking lens it is quite heavy, but not outrageously so! I have no experience of the 16-55, but I'm led to believe lol though a brilliant sharp lens, heavy. That leaves their baby brother the 18-55, which is another cracker with a variable Aperture, but nonetheless it has a very well deserved reputation!
Starting from scratch I would be very tempted by the 16-55 because it has a constant F2.8 throughout its range, it weighs about 850 grams! Reputed to equal in image quality to prime lenses. But it doesn't have the very good Fuji OIS whereas the other two do.
Until I got GAS itch for some primes, the 18-135 + 10-24 was my walkabout kit.
My lens list is 16, 23, 56, 60M, 10-24, 18-55, 18-135, 50-140 both TCs and a Samyang 300mm mirror lens, I don't contemplate lugging them all around at the same time, Sten I hope that helps.