Thicker barrels are stiffer, less affected by odd vibrations and better able to absorb heat.
Now, if you were to fire thousands of rounds in one session, the heat issue would be moot -- a bull barrel will soften and bend just like a thinner one (but not as quickly.) Now let's consider the Palma Match with 20 rounds in 20 minutes. The actual shooting is quicker, since you shoot as many rounds as possible when the wind is right -- a champion might knock out five or six rounds in less than a minute, then wait for the right wind conditions again. There, the heat absorbtion of the heavy barrel is a distinct advantage.
Finally, a heavy barrel aids in steady holding.