Interesting question.
Accuracy essentially boils down to managing variables and ensuring consistency between shots.
Thin barrels heat up more per shot than thicker barrels. Heating barrels thermally expand changing the bore dimensions. So consistency between shots is lower.
So, as is often the way, nothing is free. Losing weight costs you in lowering the ability to maintain accuracy over multiple shots.
Some people talk about "drooping" barrels with heat but if you are running your rifle fast enough to droop your barrel. You need a switch barrel system like a M60.
There are things you can do like free floating barrels, better bedding so when the barrel does expand it's not being flexed or pressured.
You can also have carbon wrapping which are more stiff to an equivalent weight solid barrel, carbon fibre is more thermally stable, and they conduct heat better, so the barrel moves less with increases in temperature and it heats more evenly - I'm not convinced they radiate heat faster necessarily, but better heat conduction does lend it self to getting more heat to the surface where it can radiate away.
You can use more thermally stable steels and ensuring the steel is stress free so expansion is more even.
Fluting may also help for similar reasons as carbon wrapped barrels but also comes with other problems.
However, you're really playing around the edges of what is essentially a physics problem.
If you want shot to shot consistency, shoot slower, cool the barrel faster, or add more thermal mass to your barrel. The ultimate goal being to try and ensure the barrel is the most similar temperature shot to shot.
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