dakotasin said:
heavy barrels:
handle heat dissipation a little better.
are less finicky about floating/bedding.
absorb felt recoil better.
tend to be installed on application specific guns, which tend to be semi-custom or modified receivers.
Heavy barrels do not dissipate heat faster. To the contrary, they dissipate it much slower that lightweight barrels. Whether that's "better" or not depends on the circumstances.
The primary advantage of a heavier barrel is that, all else being equal, the heavier barrel will be stiffer. That makes it less prone to changes in impact when pressure is applied from things like the stock, a sling, etc. Thus, as dakotasin points out, the heavier barrel will tend to be a lot less finicky about floating/bedding. If you have two identical AR's (neither free-floated) except one has a lighter barrel and the other has a heavier barrel, the lighter barrel will be more prone to changes in point of impact resulting from different amounts of pressure on the forearm, sling, etc., or even different hand positions along the forearm.
Another significant advantage of a heavier barrel is that it will heat up more slowly, and cool down more slowly, and in the process will tend to change point of impact less (again, this assumes that all else is equal, such as the specific steel, heat treating, etc.). As a barrel heats up, point of impact will change. So by slowing the rate of temperature change, you can reduce the amount by which your point of impact will shift over the course of a string of fire. Light contour barrels are famous for vertical stringing of groups, which is caused by the rapid change of temperature of the barrel. Since the heavier barrel has more mass, its temperature will change much more gradually, and stringing will be much less severe.