He is referring to how the M16 platform ended up being substantially heavier than what the original requirements laid down by the army of 6 lbs with a loaded 20 rnd mag. In the interview below Stoner talks about how the AR15 was designed around the weight requirements that were given and how he went to great trouble to meet them, and then the army got a hold of it and kept adding more and more weight which he seams to lament as it went against all the work he put into it.
You have to be careful about people's recollections, they remember what they want to remember not necessarily reality.
Fortunately, people write reports to document what really happens.
In early 1958, the Army received its first AR-15 from Armalite as part of the Small Caliber High Velocity Program. The weight of the rifle was recorded. It weighed six and a half pounds with a fully loaded 20 round magazine and sling.
It did not meet the accuracy requirement and the new stiffer (heavier) barrel was suggested.
It did not meet the barrel life requirement, a thicker barrel was suggested to help dissipate heat was suggested.
It did not meet the flash and smoke requirement and a flash hider was suggested.
It did not meet the durability requirement due to parts breakage, various improvements to parts were suggested that increased the mass of these parts.
This is not the Army being uncooperative, or adding weight just because they want to, but reporting the limitations of physics and material science*. A perfect example of this is the butt stock and hand guard nearly tripled in weight to keep them from breaking during troop trials. The end result was something that was durable enough to survive a 6,000 endurance test, and the abuse of a soldier on the bayonet course.
The Army asked for a six pound rifle for the same reason you ask $15,000 for that used car, as a starting point for the negotiation, not because you think you are going to get it for that price. The Army knew full well the first six pound rifle wasn't going to be fit for service and would gain weight during development. But, if they asked for a seven and half pound (the weight of the M16A1 at adoption) right off the bat, after development they would have had something that weighed as much as the M14.
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* The only "added extra" that the Army insisted on was the forward assist. The total weight that added to the design was 0.05 pounds, less that an ounce.