Depending on how big you want to print, Nikon or Sony full frame mirrorless with carefully selected lenses may also be an option (you can get really excellent sensors in either system). Even with good lens choices, it'll be bigger than what's been mentioned (but can be quite comparable to Fuji APS-C or the sturdier Micro 4/3 bodies). If big prints aren't the goal, you don't need anything that big. Fuji's excellent lenses (pretty much all of them) hand them the "less than full frame" image quality crown.
Nikon's Z system lenses have generally put a premium on compactness, while Sony's broader line requires care in selection. One issue with the Sony lineup is that both the 24-70 f4 "Zeiss" and the 28-70 f3.5-5.6 are from the very beginning of the FE mount, and are two of the weakest lenses in the system. The 24-70 f2.8 G-Master and the 24-105 f4 are much better lenses, but neither is small or light. If you like zooms, that's an unfortunate place to find weak lenses (the Nikon 24-70 f4 is excellent, and it is compact enough that it looks like an APS-C lens). Sony has some nice small primes in that range, and some nice wide zooms. Either one will be heavy as you get beyond ~100 mm.
So far, all bodies and lenses in the Nikon Z line have very good weather sealing, Sony less so (but improving). Both Nikon bodies, and any recent Sony body have in-body image stabilization
One especially nice thing about the Fuji system is the little 18-55 f2.8-4. It's a very small lens, and a very good one. If you're going to be out in inclement weather, remember that that particular lens isn't weather sealed, and only some bodies are (X-T1,X-T2,X-T3, X-H1,X-Pro2).. When Fuji does call something weather sealed, they mean it - I've had their sealed stuff out in pretty nasty conditions. Apart from the X-H1, they rely on in-lens image stabilization, which is often excellent, but it's spotty which lenses are stabilized. Most, but not all of the zooms are, and there are one or two stabilized primes.
