I totally agree with the suggestion about avoiding the big-name brands that charge a premium for basic plastic. I had such a bad time with a popular brand's entry level model last year... unfortunately it was just too flimsy for any real wind. It was honestly a letdown and not nearly as sturdy as I expected for the price. If you're trying to keep it cheap but actually functional for those Dolomites peaks:

• Sirui T-025SK Carbon Fiber Travel Tripod with B-00K Ball Head (really compact and light for hiking)
• Ulanzi Zero Y Lightweight Carbon Fiber Travel Tripod (if you can catch a coupon, it's basically a baby Peak Design but way cheaper) I've found that buying these slightly older models or waiting for sales is the only way to get real carbon fiber under $180. Just make sure the leg locks are tight before you head out... hate for you to have more sagging issues! Let me know if you need help finding a deal tho.

^ This. Also, totally agree with the point about not going too light. Even though the ZV-1 is a featherweight, mountain winds in the Dolomites will vibrate a thin tripod like a tuning fork. I spend way too much time looking at spec sheets and load-to-weight ratios, so here is a technical take on two others that fit your $180 budget. The SmallRig AP-02 FreeBlazer Carbon Fiber Tripod is a solid contender. It weighs around 1.1kg and uses 4-section legs instead of 5. Fewer sections usually means more stability because the bottom leg diameter stays thicker. The ball head is surprisingly decent for the price and doesnt creep as long as you arent hanging a massive telephoto lens on it. Another one is the Benro MeFoto RoadTrip Pro Carbon Fiber. Benro usually has better machining on their twist locks than the entry-level brands. It also converts into a monopod which is kinda nice for hiking. Technical wise, it handles about 8kg, so a ZV-1 wont even make it flinch. Both of these use Arca-Swiss plates which makes swapping to other gear way easier down the line. If you want me to look up the exact folded length to see if they fit your specific carry-on bag, just let me know and ill find those numbers for ya.

Just wanted to say thanks for everyone chiming in. Super helpful discussion.

Just catching up on this thread. Look, I've spent way too much money on travel gear over the years and honestly, the biggest mistake people make is going too light... even with a tiny Sony. I remember being out on a ridge in the Alps a few years back with a setup just like yours. Thought I was being smart by packing the thinnest carbon fiber legs I could find to save my back. Well, a sudden gust of wind caught the camera strap and nearly sent the whole thing... camera and all... right off a cliff. Even if the camera weighs nothing, the tripod needs some mass or at least a way to add it or the wind will just treat it like a kite. You really gotta be careful with those super thin leg sections at the bottom too. They look fine on a living room floor but get a bit of mountain grit in there or a stiff breeze and your frame is gonna wobble like crazy. Always check if there is a hook on the center column. I never shoot without hanging my bag on there now for stability. TL;DR: Don't just chase the lowest weight. If it feels like a toy, it probably is. Make sure it has a weight hook and never fully extend the center column when you're out in the wind.

Bump - same question here