Light enough for hikes, easy to travel with and sturdy enough for a 600mm f/4 is a tough call not even getting into the price issue.
FWIW, I've long used Gitzo 5 series tripods for my 600mm f/4 lenses with or without a 1.4x TC attached. These days that's fitted with a Flexshooter Pro head but I used that for years with Wimberley full gimbal heads. That setup isn't light or easy to hike with but it's rock solid when shooting such a heavy lens.
I shoot shorter lenses, landscapes and the like with a Gitzo 3 series tripod with a RRS BH-55 ball head and in a pinch or when traveling lighter I've used it to support my 600mm f/4. It can work, is certainly strong enough in the sense that I'm not worried about it unduly flexing or collapsing under load but I'll typically shoot higher shutter speeds and take more insurance bursts to ensure keepers as the setup just isn't as solid and vibration free as the bigger series 5 tripod. I've captured many sharp images with this setup but the heavier tripod is definitely nicer to work with and more stable in field use with big and heavy lenses.
But neither of those are really suitable for long hikes up into the mountains and I wouldn't really want to carry either all day long or on backpacking trips but for a few hours of work and maybe a couple of miles of walking each way they're not crazy heavy. I do have a much smaller and lighter Velbon El Carmagne 540 that I have carried on long hikes and backpacking. This still isn't tiny but is much smaller and lighter than those mentioned above. I've actually used it with my 600mm f/4 a few times and though it supports the weight safely it is much more prone to vibration issues and when I use it with the big glass I think of it more as supported hand holding or how I might think of monopod shooting rather than as a rock solid tripod that lets me get away with slower shutter speeds. It's pretty good for landscape or astro photography especially if I hang my backpack or other weight from the tripod for added stability but with the big glass it's just not nearly as vibration free as the bigger tripods.
To me the bottom line is that if you just want to take the weight of a big lens and want something more hands free than a monopod a lighter and smaller tripod can work. But if you're after rock solid stability and the ability to push your shutter speeds much lower when subject motion is minimal (e.g. owls at twilight) then the bigger tripods have a substantial advantage. Similarly shorter tripods can work but if working on hillsides or shooting up towards a nest a tall tripod makes working much more pleasant and can help increase keeper rate. So finding the holy grail of small, light (and ideally less expensive) while still getting the most out of long heavy glass is a really difficult thing if not impossible. So you sort of have to decide which tradeoffs you're willing to make.