I've been thinking of getting something like that, and I looked at the Ruger M77 Hawkeye Compacts.
They're available in .243 as well as .308 and are very small, with a 16-1/2" barrel and a shorter than normal LOP. I think they would just make your desired max weight with a scope. Blued or stainless/laminated, if you want some weather resistance.
I read somewhere that they were not aimed at the youth/small statured shooter market, though that is how they are often perceived. I understand that, as long as you provide adequate eye relief for the scope, the short LOP isn't going to bother you.
The reason that I'm chasing this idea is that I like my Ruger .44 carbine, because it is light and points quickly, but it definitely is 100yds and under and I'd like to be able to handle 150 yds (with a good rest), or perhaps a mite further.