Most of my rifles are intended to be used in a stationary context. They are also usually fired in strings of 10 or 20 rounds at a time.
Heavier barrels can absorb more heat, postponing the effects of that heat. And since I'm not lugging that rifle all over East Hell and back, the weight isn't that much of a drawback.
The heat, not so much. There ain't no such thing as a free lunch. Postponing heat effects comes at a price; cooling is likewise postponed. The rifle will continue to manifest heat related accuracy issues for a longer time than a skinny barrel, no way around that. Folks do employ barrel coolers and I'm learning that they work, too; but there's still a time overhead, even if the cooler shortens that significantly.
The skinny barrel is better for walkabout; and since they're usually shorter, too, they can be used in constricted spaces, too. Heat effects show up earlier in string fire. Their consequences can be variable based on barrel stress characteristics. That's not easily assessed before purchase, and choosing a lightweight barrel may be a bit of a crapshoot.
The better news is that lightweight barrels can dissipate that heat quicker; sometimes a lot quicker. Once in awhile, one finds a lightweight barrel that shoots as well hot as it does cool. These barrels are like Hen's teeth, to be kept and preserved as best one can.
I'm not going to attempt discussing heat absorption and rejection related to carbon barrel construction; I can't make what I consider a reliable decision on that subject.
Barrel length can be used as a means to obtain higher velocity; and conversely, to obtain the same velocity with less mayhem in the engine room.
That's how I use my 28" 260 barrel. I replaced a 24" barrel with the 28" one, and shoot it at roughly 2750fps. It's capable of another 100fps, but I don't run it there. I believe that this increases throat/bore life. I've been shooting it for 14-15 years now, so there could be some truth to the theory.
No matter what velocity you run at, you still need to deal with the same wind; and IMHO, upping the velocity vs improving one's wind skills is a bad bargain.
The key velocity is 1300fps or better at the target. The rest is about wind skills, and not about velocity. My strategy is not about fighting the wind, but about enlisting it to blow the bullet into the X Ring.
Greg