EdricBF

Having Fuji, Olympus and Sony, I would advise you to try an Olympus body: its IBIS technology is fantastic and would allow you to put that "extra-shake" behind your concerns. Or, if you really want to go Fuji, I guess you would be very happy with a 2nd-hand X-H1 (I had one and replaced it with an X-T3): it is heavier and the IBIS is also great. 
But I'd check the Olympus before anything...

Having Fuji, Olympus and Sony, I would advise you to try an Olympus body: its IBIS technology is fantastic and would allow you to put that "extra-shake" behind your concerns. Or, if you really want to go Fuji, I guess you would be very happy with a 2nd-hand X-H1 (I had one and replaced it with an X-T3): it is heavier and the IBIS is also great. 
But I'd check the Olympus before anything...

I gave up my D750 just because of its bulk and weight with FF lenses, despite being the most compact FF Nikon. Tried m4/3 for some time and found Fuji the ideal bulk/IQ/useability to me.
Although my X-T2 provides great IQ, the D750 was the best camera that I have owned since old days with a Nikon FM2n: from birds in flight to sports to kids running etc etc it never missed a shot using the Group Area AF under CAF, and its low light capbilities result in great pictures under many situations. Even family pictures taken with the integrated flash were excellent IMHO.
The X-T2 is, for me, is the "next-to-D750 big thing": it has a good Group AF, turns out excellent images but falls short comparing to the D750. If size/weight were not such an important issue, I'd go back to the D750 immediately... 

I gave up my D750 just because of its bulk and weight with FF lenses, despite being the most compact FF Nikon. Tried m4/3 for some time and found Fuji the ideal bulk/IQ/useability to me.
Although my X-T2 provides great IQ, the D750 was the best camera that I have owned since old days with a Nikon FM2n: from birds in flight to sports to kids running etc etc it never missed a shot using the Group Area AF under CAF, and its low light capbilities result in great pictures under many situations. Even family pictures taken with the integrated flash were excellent IMHO.
The X-T2 is, for me, is the "next-to-D750 big thing": it has a good Group AF, turns out excellent images but falls short comparing to the D750. If size/weight were not such an important issue, I'd go back to the D750 immediately... 

I was so disappointed with my TWO copies of the 18-135 (first one brand new, even sent to Fuji to check, the second one to confirm it was that bad...) that now I filter the reviews checking the reviewer's opinions (if any...) on that lens. Seems that people only care about the center, but for anything landscape or wider below f/8 off-center, the 18-135 sucks!!!  Any 18-55, 16-50, 18, 27 etc. "mops the floor" with it. No wonder Fuji puts an excellent IS system on it, so you can keep f/11 and high ISO most of the time... But I have seen several positive opinions, so mileage varies, of course...  

I had the 18-135 for a couple of weeks and I sold it quite disappointed of its IQ, not bad but quite lame when compared to the general fujinon quality, at least my copy. Totally another kettle of fish when pitted to the 'fijicrons' in the IQ department. Bulky and heavy BUT phenomenally good OIS and convenient range, so for video it's quite an asset. But I rather go with the usually snubbed XC16-50 zoom. It's sooo light that it's a bliss, INVALUABLY feather light when traveling, better IQ, very good wide angle range at 16mm and quite decent for video but much worst OIS than the 18-135's one (its only shortcoming). All in all a win win lens on a dirty cheap price! On the other hand the 55-200 IQ is as good as it gets, also very good OIS (almost to the level of the 18-135),quick autofocus and surprisingly good for video, a must for sports. I use it every weekend for sailing and it's a boon at an affordable price second hand (got mine for little short of 400€. So in a nutshell, grab the 50-200 and look for some light fujicrons like the 18, 35 f2 ... To my taste better to carry two small bodies like the xt10-20 and xe3 than the 18-135. By the way, very little difference in photo image quality, if at all, between the xt10 and the new XE3 but substantially better video capabilities and much better autofocus.
Any way, the 18-135 is quite a decent lens, better than most of our skills, but Fuji has better options for price/weight/IQ balance.