Without knowing your type of photography, I would guess that the 18-135 will in practice replace your 16-50 (unless you need its compactness). The 55-200 is much more an extension of what you already have. Both are fine lenses, but designed for different purposes.
The 18-135 is Fuji's version of a 'super zoom' lens: a lens with a zoom factor of at least 7x to 10x zoom. Usually these super zoom lenses suffer from a lot of compromises, but this is actually quite a good one with good 'sharpness' and contrast except perhaps for the far corners and edges. It's a true 'travel lens' that for many people is almost 'glued' to their camera. Together with the 10-24 you'd have a very universal combo. However, don't expect it to have 'exquisite bokeh' and shallow depth-of-field for portraits. Around 50mm the max. aperture is f5, so the DoF can't be really shallow. The OIS is very good so the smaller apertures can be compensated with longer shutter speeds without blurred images due to camera shake.
The 55-200 is a true tele zoom lens. Not a lot of people need the longer focal lengths (beyond 200mm in full frame equivalent terms or 135mm in Fuji's APS-C format), but if you do -like for sports, wildlife or landscape details- it's a very good lens. In pure sharpness it even 'beats' Fuji's professional 40-150 tele zoom, but that one has a bit better contrast and a constant f2.8 aperture. I would not worry too much about the Weather Resistance (WR) thing. First, your camera isn't WR, so that is the limiting factor. Secondly, if you take a few precautions, also non-WR lenses can be used in a light drizzle or rain without you worrying about it. My guess is that you're not the photo reporter waiting in the downpour for that perfect shot in a football match. The OIS in the 55-200 however, is very useful when you start zooming in. At 200mm (300 in full-frame) it becomes hard to carefully focus and keep a steady shot.
I agree with Lrover. The 18-135 is my go-to lens for travel and just everyday shooting. Also, being WR, it is good out doors in all kinds of weather. The wide range of focal lengths makes it very handy. Take a look at the YouTube video by Andrew and Denae as Andrew goes over all the fuji lens and why he likes each one and for what.
Depends of course on what you are shooting. I have both and they are fine lenses. I find that I use the 18-135 far more than the 55-200. The 18-135 is a great all round lens producing some surprisingly good images. Also nice and light to carry, well balanced on XT4.