I have a pair of Leica 10*42 Trinovids, which I’ve had for 30 years and have used extensively for bird-watching. Fabulous optics, and would cost me €1000 to replace; however, due to that fact, and the weight factor, I always take another, much less costly, and lighter, binocular if I’m hiking in the hills.
Look for folding binoculars to save on space in the rucksack: after losing a pair a couple of years ago, I settled on a pair of Nikon Akulon A30 10*25’s by searching online. They’re pretty good for the price (GBP50 - 60), they’re rubber-armoured, have extending eye-caps for spectacle wearers, are at least rain-resistant, and they’re cheap enough to lose, or break, or give away, and at 270 grams not what I would call heavy, compared to the Trinovids at about 750 grams - dont buy anything TOO light, or they’ll end up being flimsy. Also don’t get anything too cheap or the optics will be poor, which might be OK in bright sunshine, but when it’s overcast or hazy, or the sun is low in the sky, the last thing you want to be battling on the hill is poor optics when you’re trying to find signs of a path in the distance.
You could of course go for a monocular if you really want to save on space and weight, and I used one many years ago, but they’re not so easy to find, field of view tends to be rather limited, they’re a bit fiddly, and somehow easier to drop!
EDIT - just read your post again, and I see you’re interested in viewing the other summits around you. Then, I’d definitiely go for 1025’s or 1020’s, the 10 being the magnification factor, and important when viewing more distant objects. 825’s or 820’s, with their more gentle magnification, would be more suited to closer-range viewing - say, viewing birds while walking in the forest - than for more distant objects.