The bullets my buddy swages for me uses J4 jackets from Berger. These jackets are swaged from a piece of flat copper, drawn into a cup, and then swaged down to caliber. The final step in the process forms the final length of the jacket and trims off the excess. Most jackets we use are within .01 grain in weight.
We use a special die that forms the lead core that goes into the bullet. Pure lead is extruded in wire form and cut to length. We drop it in the form die and it is compressed to caliber. Excess lead is actually extruded thru the side of the die and looks about like #5 pencil lead when it drops off. These lead core weight exactly the same each time.
The bullet jacket and core are dropped into the core seating die. The core is seated into the jacket and is pressed out to fill the jacket and form the boattail (if using the boattail die) or flat base. The seated core/jacket then goes into the point form die. The point form die closes the jacket and makes the tip. The size of core used will determine the bullet weight.
Each step in the process, the jacket, core, seated core, pointed bullet all have to come back out of the die. The bullet jackets have a very fine lube on them. Each die has a "punch" that pushes the core or jacket out of the die. The nose forming die has a very fine pin that pushes the bullet out from the point. This die is usually adjusted so the pin will just enter the hollow point and push against the softer lead to push the bullet out. The softer lead is more forgiving than the copper jacket so less chance in bending the pin.
There is another die that can be used. Most bullet makers do use it, most sportsmen don't fork out the extra dough to buy it. The additional die closes up the hollow point of the bullet. If there is excess lead, this makes the lead soft points. If the bullet has one of the polymer tips, this is when the tip is put in. My buddy and I, we can live with the slightly larger hollow point.
Our bullets are usually within .01-.02gr. If you check with the bullet makers, whose bullets are made on more complex machines, their bullets are usually +/- .03 grains. Sometimes +/- 3%. It depends on their specifications.
A bullet in flight has an "airstream" around it. Pointier bullets cut the "air" better than flatter point bullets. Once the bullet point gets down to a certain size per caliber (and I don't know what this is) point size does not make a lot of difference. Base of the bullet also has an affect on the "airstream" during flight. I am not an expert on this, but if you read some of the information from benchrest shooters, they know which distance by caliber where flat base bullets become less stable and where boattail bullets continue to be stabilized.
I have shot our swaged 6.5 142gr HPBT bullets against Speer, Sierra, and other bullets in competition. My group sizes are right in there with the best of the best. Berger VLD bullets in the PPCs do a little better, but design and stability is probably better too.
Lots of info in internet land on bullet manufacturing. Richard Corbin at RCE Corp has been instrumental in helping us make our jacketed bullets cheaper than buying them and in most respects with better uniformity and accuracy. Don't get compensated for time, but that is why they call it a "hobby".
Top photo is 6.5mm 120gr bullet made from 22 mag brass. Note the flat tip. This is hollow point. Flat tip is approximately size of the pin in the point form die used to punch out the bullet. Bottom photo is picture of different bullet ogives. You can see as the ogive increases, the bullets will cut the air better.
Have fun!!
Steve