As stated you can only go so far. I homebrewed a Savage 110 in .243 a couple years ago with an 18.5" McGowan Striker barrel from savagebarrels.com, a Boyd's lightweight laminated thumbhole stock and Redfield 2-7x scope and it's still not what I'd call a lightweight. I do think the el'cheapo Choate (?) stock I had on it before hand was lighter but I've never scaled em out to be sure. But other than that you're gonna have what ya have and either that or stay home.
BTW, the main advantage of the shorter barrel is not in the weight savings. Just makes for a quicker handling gun with different balance that catches less crap when you're in the thick stuff.