I think I posted this a couple years ago, a .338 Lapua (Norma might be a better match) medium machine gun, weight is comparable to standard (Nato*) 7.62x51mm mgs, range is closer to a .50 caliber.
http://www.thefirearmblog.com/blog/2017/10/09/338-firepower-hands-gdlss-lightweight-medium-machine-gun-ausa-2017/
Perfect weapon for a Dark Champions character...
http://www.thefirearmblog.com/blog/2017/10/09/7-62mm-lightweight-machine-gun-unveiled-knights-armament-company/
also early development of a 7.62 MG that is estimated to weigh about 12-13 lbs. Even if beefed up to 14 for greater durability, still an improvement. If they combined this with the stainless/aluminum hybrid cases that allow carriage of 5 rds loaded instead of 4, and the new M80A1 load's lighter bullet, might be able to drop a bit of weight for the troops, while still allowing 7.62 power and range.
I think in the long term the CTA program's 6.5mm might be a better choice, but staying with 7.62 has its own advantages.
*The reason I note NATO mgs, is because some russian ones are lighter. I have only fired a few rounds through an M60, and have no experience with ANY of its competitors.