A heavy (varmint) barrel will tend to be a little more rigid, and take a little longer to heat up. They weigh more than a sporter weight, and tend to be more steady on a rest. They tend to dampen harmonics better than a lighter weight barrel also. Do they shoot that much better in the sizes issued by the major manufacturers than a standard weight barrel? Probably not a great deal of difference in most cases. There are lots of skinny, whippy-tubes out there that shoot just as well.
If you like the looks of it, and feel it may help improve your shooting, then go for it. I just really don't feel that a heavy barreled varmint rig is going to guarantee you get what you thought it would. Also, don't forget the added weight you will have to lug around unless you park yourself at the edge of a field when you go out. Just my opinion..........