If you stick to AR pattern DI it won't be hard. Take a BCL 102 with a lightweight HG and re-barrel. They weigh 9 lbs, two mods and you're just into the 7.9 lb range with sub-MOA accuracy. My factory rig seemed better than others that have posted their results here ( if you check my posts from earlier in the year, I shot sub-MOA with 168 GMM ) , but with a Criterion lightweight I think anyone's 102 will show sub-MOA accuracy and consistency. The Faxons are light, accurate, stress relieved as well. I shoot lots of surplus so I stuck with 308, but you could always go 6.5 CM if ammo cost is less of a concern.
Lightweight Handguard - Go with one of the ultra lightweight ones you can remove up to about 14 oz vs my first run 102 HG. The newer 102's might have lighter HG's so take those numbers with a grain of salt. The SLR Helix and Odin O2 are super light.
Lightweight Barrel - The factory BCL 102 barrel is 2 lb 12 oz. You can get that down to 2 lb 6 oz with the 18.5" Criterion lightweight or 2 lbs 4 oz with a Faxon lightweight 20" (their real world weights are a couple oz heavier than claimed) . That removes another 6-8 oz.
You could lose a little on the BCG or stock, although the factory stock is already very light (about 9 oz). I chose to go slightly heavier stock with a +3 oz gain in the fixed MOE, I wanted to balance the gun a bit and a fixed for reliability. I also didn't want to bother with potential reliability/cycling issues and cost of the lightweight BCG's so I kept it stock. But potentially you could get the gun in that 7.5 lb real world range. And don't trust the claimed weights because 95% of the time they are out by a couple oz. My weights above are confirmed on an accurate digital scale, not a bathroom scale.
