When the Marines first arrived at the Front in WWI, the Germans moved within 100 yards and began setting up camp for the evening. Naturally, the Marines began picking them off, probably with the 30-06 1903 Springfield with iron sights.
So the Germans moved back 100 yards and started to set up camp. Marines resumed fire. The Germans kept moving back until, at 600 yards, the Marines gave it a rest.
With the M-14 (yeah, I know, 7.62 vs 30-06, but similar performance) I put 7 of 10 rounds in a 12 inch bull from 200 yds, Standing and also 7 of 10 in a 20 inch bull from 500 yards, Prone - all with iron sights.
As to weight of the weapon - that is not the issue. The weight of the ammo is what makes the biggest difference. In Vietnam I carried 500 rounds of 5.56 - as field radio operator. 500 rounds of 7.62 or 30-06 weighs about twice as much as 5.56.
You're not quite telling the whole story. That PRC25 or PRC77 radio was another 15 pounds, plus the handset and antenna. Plus your water, and Crations or LRRPS for lunch. And supper. or breakfast.
a 250-round can of linked 7,62 mg ammo is 18 pounds, one reason they cut them back to 200 rounds in canvas bandoleers and cardboard boxes. So adding in 8 pounds of M16A1, you were humping at least 50, 60 pounds, water weighing in at around 7 pounds/gallon. Oh, and your helmet and flak jacket, mustn't forget those....