The Heavyweight...180 grains.
In the early part of the 20th Century, when the '06 was first getting it's legs under it, bullets looked much the same as they do today on the exterior- except they were far different internally. The jackets tended towards thin and the bonding process common today in which the bullet jacket and core are molecularly bonded together was still several decades off. Those early bullets when pushed to previously unheard of velocities by smokeless powder quite frequently just came apart on impact. Ballistic engineers back then handled that in a couple of ways. The first was to simply make the bullet "full patch" or as we know it- "full metal jacket" in which the bullet is designed for zero expansion by virtue of a continuous gilding metal jacket. Such ammunition was frequently used in sporting applications back then but serious wounding and slow, sloppy kills were the result. In modern times this type of ammunition is frequently prohibited by law for hunting and common decency prevents us from using it in the few places where it is legal outside of very special applications in which it is appropriate.
The other way they helped that bullet survive the impact velocity is of more interest to us. They simply made it heavier. Where the 150gr could hit 2950 fps and often ruptured on close shots, engineers made the bullet 180grs which slowed it down to 2650 or 2700 fps or so. The result is one of the most splendidly boring ballistic combinations ever devised by man. The bullet would survive an almost point blank hit and if it did rupture the fragments were large enough to be effective on their own. Penetration was greatly increased and hunters soon learned that two holes are better than one when it comes to letting hot blood out and cold air in. In fact, for a guy switching over from the .30WCF or even one of the big black powder rounds the amount of penetration was staggering from the these heavy for caliber bullets at moderate speeds. This result was not only great on big bodied deer but on elk, moose, bears...you name it. The 180gr@2700fps was THE cartridge that made the '06's reputation as a game cartridge. When combined with a rifle scope the American hunter was deadly to previously unheard of distances on larger game than ever before and the cartridge became a worldwide success and today counts for an enormous number of game animals.
In my own experience I've used it and it works. In my test rifle the 180gr. Corelokt produced groups of 2" with regularity- good, but not stellar, although one would have to come up with a pretty bizarre scenario where that wouldn't suffice as a hunting rifle to typical ranges. Performance on game was perfected decades ago and most .30 caliber 180gr projectiles are made to function at '06 speeds to perfection and most deliver the goods. As far as gun writing goes this whole bit makes me want to yawn in the worst way. Effective, cheap and plentiful is how I'd describe the 180gr '06 cartridge.
I do find it interesting that people insist on using the newer, tougher projectiles in the 180gr '06. Really tough bullets like the TSX, Bear Claw and Etip- those bullets are made for magnum speeds not the plodding velocity the '06 generates. Plain Jane cup and core bullets for the '06 have been around for a century and were perfected a generation or two ago. There is simply no replacing the sheer amount of R&D and real world experience that has went into .30-06 ammo...regardless of what the marketing message might tell you.
And speaking of marketing...
The Middleweight ...165 grains.
A fairly new product, the .30-06 (and .308) 165 gr bullet was touted as being the ultimate compromise in velocity and bullet weight. Let's be honest here- there isn't enough trajectory and velocity difference to make any of these more appealing than the other. The difference between the 150, 160, and 180gr over 300 yards isn't more than a couple of inches and no one can typically hold that in the field anyway. Bullet performance is likewise uniform since we figured out how to taper and bond bullet jackets long before the 165gr load saw the light of day. It is there though and has gained acceptance in the marketplace although I think the 165gr weight is best served in the .308 Winchester since it's short on case capacity to shoot the 180gr to really useful velocities. There is no reason to overlook it in the '06 if you have a rifle that likes it though, but it really doesn't serve much of a technical purpose. It shoots almost as fast as the 150, it kicks a little less than the 180... but the only real difference is on the ballistic table and you can't kill anything with one of those.
My rifle shot it pretty much the same as the 150 and 180gr. and while there is nothing really wrong with it; you sure don't gain much range over a 180 and you sure don't get much more bullet than the 150gr. It may be my old age showing, but I just can't think of a real advantage for it. It is, for all practical purposes, the answer to a question no one asked.
In reality, outside of my traditionalistic prejudices, the '06 shooter will be well served shooting either 150, 165 or 180 grain bullets of good quality for almost anything that walks in N.America and most other places. If I had moose or elk on the menu (or hunted in serious bear country) I'd lean toward the 180 and if I primarily hunted eastern White-tailed deer or antelope I'd lean to the 150 but there really are no wrong answers if the hunter is a good shot and gets to practical range. Shot placement and bullet construction trumps everything else and the '06 has a lot of offer there.