Wilson Combats Lightweight barrel used to be the "lightest". I have one and completely changed my gun. After quick rounds it seems the groups open up.
Now Wilson Combat makes a Ranger barrel, it is heavier than my Lightweight but still their lightest weight barrel.
ARP also makes a good light-ish weight barrel.
You will also save weight with the handguard, stock, optic and optic mount. Also a titanium suppressor really helps.