There is no "one size fits all" rifle weight. The heavier/faster the bullet you're shooting... the more weight you will want to mitigate the recoil for maximum shootability. This is one reason why you'll see a lot of "rokslide" specials out there (223 tikka) because they offer minimum recoil and are easy to shoot accurately (not to mention the ammo is cheap, so you can practice more). In contrast, if I were shooting a 7BC or 7RM, or 300WM, etc... I would want a heavier rifle system.
I say "system" because the weight of the rifle itself is only part of the overall weight that is ultimately attached to the rifle (and that you will also be lugging up the hill).
The lightest weight dialing scope, with side focus, and at least a 10x top end will end up around 25oz once you put it in rings and add scope caps. However, if you want more features, longer zoom, bigger objective, etc... you'll likely be pushing 28-30oz at a minimum.
Decent suppressors will be anywhere between 5oz and 17oz
A decent lightweight Bipod or Tripod weighs between 6oz and 32oz... and will greatly depend on the style of hunting/shooting positions you plan for.
Drop mags between 2 and 8oz, and the extra ammo in an ammo sleeve could add 6-10oz.
It all adds up...
I like the lightest-weight hunting system that I can buy or create that is ALSO suitable for an effective hunt.
For example... I've got a truly "ultralight" 223rem rifle system (2.25lbs bare rifle) and it was used by several kids last fall to harvest four elk (each with one shot, out to 330 yards). It is perfect for hunts where Im taking kids who arent experienced enough to shoot beyond a few hundred yards anyway. However, due to its long range limitations (wind drift, light splash, etc) it's not the rifle I'd grab if I were planning a backcountry hunt where I might encounter a variety of longer range shot opportunities with competent shooters... I'd want something in a 6mm or 6.5mm with a higher BC bullet. But inevitably... that bigger caliber brings more recoil than the little 223rem... so those rifle systems will weigh more.
But... its pretty meaningless to shave a few ounces off your rifle system if everything else in your pack is heavy. So, as it's been noted... that's the best place to start. Literally weigh everything you carry up the hill, from your shoes to your water bottle to your pocket knife... and consider what items are redundant and can be left home, and what items can be swapped for a lighter-weight version without losing essential functionality.
Here are some ultralight rifle setups... 223rem, 22 creed, 6mmCreed, 6.5CM. Most are under 5lbs bare rifle, several under 4lbs. These rifles have taken over 50 elk, deer, bears, and wolves in the past 5 years. Not a single animal lost/wounded... The vast majority of the shots taken were in the hands of kids, with one shot, 250-450 yards. More than a few were in the 500+ yard range... which I know... for RS guys isn't all that far... but in real backcountry conditions, deep in an Idaho wilderness... it's pushing our limits.
