It depends on the amount of shots that you want to take. The idea behind o heavy barrel is stiffness obviously and the amount of time it takes to heat up. Another option is to flut it. If you don't take a huge string of shots in a row, why carry the weight and this isn't target competition, so the slight accuracy to be had off a heavy vs featherweight isn't that great. If you are shooting lots of shots in a row such as in a big dog town, you need to think about barrels heating up. Also heavy rifles are supposed to be steadier for off hand positions, but lighter swing faster (correct?). I couldn't ever shoot well off hand and haven't taken the time to learn the tricks.

That being said, both of my varmit rifles carry heavy wieght barrels. I shoot more prairie dogs than coyote. I'm also in my late twenties and am fit. I carry the rifle a short distance (500 yds commonly) before I set up to start shooting. Rarely is rifle weight and issue, more times it is a lack of hands to carry the spotting scope, several boxes of shells, rifle, mat, water, etc.