I do not make barrels but I have installed many hundreds of them. I have worked with barrelmakers and spoken with others.
The stress in barrels comes from two sources. The first source is the barrel steel itself. Although this steel is generally purchased as "stress-relieved" there is some variation between batches and, indeed, within the same batch. Many makers will stress reliev again after the blank is cut to length but before it is drilled or reamed.
The second source of stress is that which is imparted during the manufacturing process. In general. this applies mostly to button rifled barrels wherein the rifling is cold swaged into the bore. For this reason, most manufacturers of button rifled barrels stress relieve after rifling but prior to contouring.
Cryo treatment, the freezing of barrels by immersion in liquid nitrogen, has not been shown to accomplish anything with regards to stress relief. It does appear to improve machinability to a certain extent although there is still considerable debate on that issue as well.
Hammer forged barrels are remarkably inert because the molecular structure is affected by the forging process. In addition, those barrels come out of the machine smokin' hot and are kind of self relieveing.
Contour of the barrel is determined by the intended use of the rifle and the type. In some cases, rigidity is of paramount concern so the barrel is made heavy and not too long. In another case, it may be considered to be OK to sacrifice some rigidity in exchanged for the higher velocity produced by a longer barrel. A shorter barrel improves portabilty and quickens handling. A longer barrel makes the rifle hold steadier and smooths out the swing on running shots.
How the rifle balances is greatly affected by the taper of the barrel. In oither words, not just the weight but where the weight is carried. If the weight is toward the muzzle, the rifle is muzzle heavy and will handle more slowly. If the weight is further back or between the hands, the rifle will be quicker handling although the two rifles may weigh exactly the same.
A lighter barrel really will cool off more quickly than will a heavy one. It is good that this is so because it will also heat up much more quickly. So, in ten shots, the heavy barrel will have absorbed "x" number of btu's but this amount of heat will have raised the temperature of the barrel to a certain level. A lighter barrel will have absorb the same btu's but since there is less mass to heat, the temperature will be much higher.
The extra weight will dampen vibrations and the heavy rifle will be less affected by recoil forces and the hold.
Small variations in contour will have a greater effect on handling and appearance than they will on actual accuracy potential. The choice of a particular contour is, once again, dependent upon the intended purpose of the rifle and the handling chactaristics desired. If a rifle is to be used with a bipod, it probably doesn't matter since any balance has gone out the window anyway! GD